existence of solutions to a model for sparse one dimensional fluids abstract we prove the global existence of solutions to a model for a viscous compressible barotropic fluid initially occupying a general open subset of a finite one dimensional interval the fluid equations are applied only on the support of the density understood in the sense of distributions this support must be tracked and accommodation must be made for the possibly infinite number of collisions of fluid packets occurring on a possibly dense set of collision times our approach avoids certain nonphysical properties of solutions which are constructed as limits of solutions in which artificial mass has been inserted

surfaces of general type with p_g q 1 k 2 8 and bicanonical map of degree 2 we classify the minimal algebraic surfaces of general type with pg q 1 k 2 8 and bicanonical map of degree 2 it will turn out that they are isogenous to a product of curves i e if s is such a surface then there exist two smooth curves c f and a finite group g acting freely on c x f such that s c x f g we describe the c f and g that occur in particular the curve c is a hyperelliptic bielliptic curve of genus 3 and the bicanonical map of s is composed with the involution induced on s by r x id c x f c x f where is the hyperelliptic involution of c in this way we obtain three families of surfaces with pg q 1 k 2 8 which yield the first known examples of surfaces with these invariants we compute their dimension and we show that they are three generically smooth irreducible components of the moduli space m of surfaces with p g q 1 k 2 8 moreover we give an alternative description of these surfaces as double covers of the plane recovering a construction proposed by du val

omnibus tests for comparison of competing risks with adjustment for covariate effects summary this article develops omnibus tests for comparing cause specific hazard rates and cumulative incidence functions at specified covariate levels confidence bands for the difference and the ratio of two conditional cumulative incidence functions are also constructed the omnibus test is formulated in terms of a test process given by a weighted difference of estimates of cumulative cause specific hazard rates under cox proportional hazards models a simulation procedure is devised for sampling from the null distribution of the test process leading to graphical and numerical techniques for detecting significant differences in the risks the approach is applied to a cohort study of type specific hiv infection rates

the chen ruan cohomology of moduli of curves of genus 2 with marked points in this work we describe the chen ruan cohomology of the moduli stack of smooth and stable genus 2 curves with marked points in the first half of the paper we compute the additive structure of the

a class of k sample tests for comparing the cumulative incidence of a competing risk in this paper for right censored competing risks data a class of tests developed for comparing the cumulative incidence of a particular type of failure among different groups the tests are based on comparing weighted averages of the hazards of the subdistribution for the failure type of interest asymptotic results are derived by expressing the statistics in terms of counting processes and using martingale central limit theory it is proposed that weight functions very similar to those for the g p tests from ordinary survival analysis be used simulation results indicate that the asymptotic distributions provide adequate approximations in moderate sized samples

the graphical evaluation of explanatory variables in proportional hazard regression models summary a graphical technique for assessing explanatory variables in cox s proportional hazards regression model is examined the method arises from consideration of the cumulative hazard transformation and the partial likelihood score function and consists of permuting the observed rank statistic to account for the effects of explanatory variables fitted to the model an example is provided

very ampleness and the infinitesimal torelli problem according to p griffiths an important problem in higher dimensional geometry is to find classes of complex varieties of general type x for which the infinitesimal torelli map is injective his deep ideas are at the origin of a large literature if dim x 1 very ampleness of the canonical sheaf is a sufficient condition in this paper we prove that for any natural number n 5 there exists a generically smooth irreducible n 9 dimensional component mathcal s n of the moduli space of algebraic surfaces such that for a general element x of mathcal s n the canonical sheaf is very ample and the 2 infinitesimal torelli map d phi 2 h 1 x t x longrightarrow rm hom left h 2 0 x h 1 1 x right has kernel of dimension at least 1 this shows that contrary to the curve case the task of finding conditions which imply the injectivity of the infinitesimal torelli map is very open

second chern class of fano manifolds and anti canonical geometry let x be a fano manifold of picard number one we establish a lower bound for the second chern class of x in terms of its index and degree as an application if y is a n dimensional fano manifold with k y n 3 h for some ample divisor h we prove that h 0 y h ge n 2 moreover we show that the rational map defined by vert mh vert is birational for m ge 5 and the linear system vert mh vert is basepoint free for m ge 7 as a by product the pluri anti canonical systems of singular weak fano varieties of dimension at most 4 are also investigated

characterization of the 4 canonical birationality of algebraic threefolds for nonsingular projective threefolds x of general type whose geometric genus p g h 0 x k x is ge 5 the birationality of the fourth canonical map varphi 4 x phi 4k x was characterized by d q zhang and the first author in 2008 this paper aims at characterizing the birationality of varphi 4 x for those x with p g 4

on rigid compact complex surfaces and manifolds abstract this article investigates the subject of rigid compact complex manifolds first of all we investigate the different notions of rigidity local rigidity global rigidity infinitesimal rigidity etale rigidity and strong rigidity and the relations among them only for curves these notions coincide and the only rigid curve is the projective line for surfaces we prove that a rigid surface which is not minimal of general type is either a del pezzo surface of degree 5 or an inoue surface we give examples of rigid manifolds of dimension n 3 and kodaira dimensions 0 and 2 k n our main theorem is that the hirzebruch kummer coverings of exponent n 4 branched on a complete quadrangle are infinitesimally rigid moreover we pose a number of questions

vector bundles of rank 2 and linear systems on algebraic surfaces let s be a smooth complex algebraic surface and let l be a divisor on s it is well known that the linear system il ksi where ks is the canonical divisor plays an important role in understanding the geometry of s several authors see for example 8 11 studied various properties of this system our paper treats the same subject but the point of view is different from the works mentioned above the philosophy underlying our approach is almost classical points on s more generally effective 0 cycles in special position with respect to il ksi see definition below contain information about the geometry of s this point of view was recently revived in 5 also 10 in fact this paper contains the technique of going from the effective 0 cycle z in special position with respect to il ksi to the geometry of s for the sake of completeness we give a definition and state a theorem which can be found in 5 10

quotients of products of curves new surfaces with pg 0 and their fundamental groups we construct many new surfaces of general type with q pg 0 whose canonical model is the quotient of the product of two curves by the action of a finite group g constructing in this way many new interesting fundamental groups which distinguish connected components of the moduli space of surfaces of general type we indeed classify all such surfaces whose canonical model is singular the smooth case was classified in an earlier work as an important tool we prove a structure theorem giving a precise description of the fundamental group of quotients of products of curves by the action of a finite group g

on the projective normality of double coverings over a rational surface abstract we study the projective normality of a minimal surface x which is a ramified double covering over a rational surface s with dim k s 1 in particular horikawa surfaces the minimal surfaces of general type with k x 2 2 p g x 4 are of this type up to resolution of singularities let be the covering map from x to s we show that the z 2 invariant adjoint divisors k x r a are normally generated where the integer r 3 and a is an ample divisor on s

a numerical criterion for very ample line bundles let x be a projective algebraic manifold of dimension n and let l be an ample line bundle over x we give a numerical criterion ensuring that the adjoint bundle kx l is very ample the sufficient conditions are expressed in terms of lower bounds for the intersection numbers l y over subvarieties y of x in the case of surfaces our criterion gives universal bounds and is only slightly weaker than i reider s criterion when dimx 3 and codimy 2 the lower bounds for l y involve a numerical constant which depends on the geometry of x by means of an iteration process it is finally shown that 2kx ml is very ample form 12n our approach is mostly analytic and based on a combination of hormander s l estimates for the operator lelong number theory and the aubin calabi yau theorem

on birational geometry of minimal threefolds with numerically trivial canonical divisors for a minimal threefold x with k x equiv 0 and a nef and big weil divisor l on x we investigate the birational geometry inspired by l we prove that ml and k x ml give birational maps for all m ge 17 the result remains true under weaker assumption that l is big and has no stable base components

smoothed nonparametric estimation for current status competing risks data we study the nonparametric estimation of the cumulative incidence function and the cause specific hazard function for current status data with competing risks via kernel smoothing a smoothed naive nonparametric maximum likelihood estimator and a smoothed full nonparametric maximum likelihood estimator are shown to have pointwise asymptotic normality and faster convergence rates than the corresponding unsmoothed nonparametric likelihood estimators using the smoothed estimators and the plug in principle we can estimate the cause specific hazard function which has not been studied previously we also propose semi smoothed estimators of the cause specific hazard as an alternative to the smoothed estimator and demonstrate that neither is uniformly more efficient than the other numerical studies show that a smoothed bootstrap method works well for selecting the bandwidths in the smoothed nonparametric estimation the use of the estimators is exemplified by an application to cumulative incidence and hazard of subtype specific hiv infection from a sero prevalence study in injecting drug users in thailand copyright 2013 oxford university press

surfaces of general type with pg 0 k2 6 and non birational bicanonical map let s be a minimal surface of general type with p g 0 and k2 6 such that its bicanonical map open image in new window is not birational the map is a morphism of degree 4 onto a surface the case of deg 4 is completely classified in topology 40 5 2001 977 991 and the present paper completes the characterization of these surfaces it is proven that the degree of cannot be equal to 3 and the geometry of surfaces with deg 2 is analysed in detail the last section contains three examples of such surfaces two of which appear to be new

semiparametric models for cumulative incidence functions in analyses of time to failure data with competing risks cumulative incidence functions may be used to estimate the time dependent cumulative probability of failure due to specific causes these functions are commonly estimated using nonparametric methods but in cases where events due to the cause of primary interest are infrequent relative to other modes of failure nonparametric methods may result in rather imprecise estimates for the corresponding subdistribution in such cases it may be possible to model the cause specific hazard of primary interest parametrically while accounting for the other modes of failure using nonparametric estimators the cumulative incidence estimators so obtained are simple to compute and are considerably more efficient than the usual nonparametric estimator particularly with regard to interpolation of cumulative incidence at early or intermediate time points within the range of data used to fit the function more surprisingly they are often nearly as efficient as fully parametric estimators we illustrate the utility of this approach in the analysis of patients treated for early stage breast cancer

a sharp lower bound for the canonical volume of 3 folds of general type let v be a smooth projective 3 fold of general type denote by k 3 a rational number the self intersection of the canonical sheaf of any minimal model of v one defines k 3 as the canonical volume of v assume p g v 2 we show that k 3 ge frac 1 3 which is a sharp lower bound then we classify those v with small volume we also give some new examples with p g 2 which have maximal canonical stability index finally we give an application to 4 folds of general type

existence and uniqueness of small energy weak solution to multi dimensional compressible navier stokes equations with large external potential force we study the 3 d compressible navier stokes equations with an external potential force and a general non decreasing pressure we prove the global in time existence of weak solutions with small energy initial data and with densities being non negative and essentially bounded a solution may have large oscillations and contain vacuum states no smallness assumption is made on the external force nor the initial perturbation in l for density initial velocity u0 is taken to be bounded in lq for some q 6 and no further regularity assumption is imposed on u0 finally we discuss the uniqueness of weak solutions

classification of quadruple galois canonical covers i in this article we classify quadruple galois canonical covers of smooth surfaces of minimal degree the classification shows that they are either non simple cyclic covers or bi double covers if they are bi double then they are all fiber products of double covers we construct examples to show that all the possibilities in the classification do exist there are implications of this classification that include the existence of families with unbounded geometric genus in sharp contrast with triple canonical covers and families with unbounded irregularity in sharp contrast with canonical covers of all other degrees together with the earlier known results on double and triple covers a pattern emerges that motivates some general questions on the existence of higher degree canonical covers some of which are answered in this article

on the adjunction mapping of very ample vector bundles of corank one let e be a very ample vector bundle of rank n 1 over a smooth complex projective variety x of dimension n 3 the structure of x e being known when k x det e 0 we investigate the structure of the adjunction mapping when 0 k x det e n

on irregular threefolds and fourfolds with numerically trivial canonical bundle we prove that for a smooth projective irregular threefold x with k x equiv 0 and a nef and big divisor l on x ml p gives a birational map for all m ge 3 and all p in mathrm pic 0 x we also use the same method to deal with fourfolds and prove that for a smooth projective irregular fourfold x with k x equiv 0 and an ample divisor l on x ml p gives a birational map for all m ge 5 and all p in mathrm pic 0 x these results are optimal

murphy s law in algebraic geometry badly behaved deformation spaces we consider the question how bad can the deformation space of an object be the answer seems to be unless there is some a priori reason otherwise the deformation space may be as bad as possible we show this for a number of important moduli spaces more precisely every singularity of finite type over up to smooth parameters appears on the hilbert scheme of curves in projective space and the moduli spaces of smooth projective general type surfaces or higher dimensional varieties plane curves with nodes and cusps stable sheaves isolated threefold singularities and more the objects themselves are not pathological and are in fact as nice as can be the curves are smooth the surfaces are automorphism free and have very ample canonical bundle the stable sheaves are torsion free of rank 1 the singularities are normal and cohen macaulay etc this justifies mumford s philosophy that even moduli spaces of well behaved objects should be arbitrarily bad unless there is an a priori reason otherwise thus one can construct a smooth curve in projective space whose deformation space has any given number of components each with any given singularity type with any given non reduced behavior similarly one can give a surface over mathbb f p that lifts to p 7 but not p 8 of course the results hold in the holomorphic category as well it is usually difficult to compute deformation spaces directly from obstruction theories we circumvent this by relating them to more tractable deformation spaces via smooth morphisms the essential starting point is mnev s universality theorem

on positivity of line bundles on enriques surfaces we study linear systems on enriques surfaces we prove rationality of seshadri constants of ample line bundles on enriques surfaces and provide lower bounds on these numbers we show the nonexistence of k very ample line bundles on enriques surfaces of degree 4k 4 for k 1 thus answering an old question of ballico and sommese introduction in this note we answer a question posed by ballico and sommese 1 see also terakawa 14 concerning the existence of k very ample line bundles of degree 4k 4 on enriques surfaces we show that such line bundles exist if and only if k 0 and that in fact the degree of a k very ample line bundle on an enriques surface is subject to a much more restrictive bound theorem 2 4 this has strong consequences for the local positivity of line bundles on enriques surfaces we address this questions in section 3 in particular we show that seshadri constants of ample line bundles on enriques surfaces are always rational 1 auxiliary material and notation the basic reference for this paper is the monograph 6 by cossec and dolgachev here we briefly recall properties of enriques surfaces needed for our considerations first of all an enriques surface is a surface y of kodaira dimension zero with no differential forms in particular ho ky 0 and the canonical bundle ky is a 2torsion element in pico y i e 2ky oy to alleviate notation it is convenient to use the following convention in the sequel we make frequent use of vanishing theorems and statements on adjoint line bundles since the canonical divisor ky is numerically trivial the adjoint line bundle ky l has the same numerical properties as l in particular if l is nef and big ample then so is ky l by the nakai moishezon criterion so in order to get vanishing statements for l we apply vanishing theorems to ky l and use the fact that 2ky is trivial in the sequel we do so without comment and hope to cause no confusion this way received by the editors june 1 2000 2000 mathematics subject classification primary 14j28 secondary 14c20 14e25

global solutions of the navier stokes equations for multidimensional compressible flow with discontinuous initial data abstract we prove the global existence of weak solutions of the navier stokes equations for compressible isothermal flow in two and three space dimensions when the initial density is close to a constant in l 2 and l and the initial velocity is small in l 2 and bounded in l 2 n in two dimensions the l 2 norms must be weighted slightly a great deal of qualitative information about the solution is obtained for example we show that the velocity and vorticity are relatively smooth in positive time as is the effective viscous flux f which is the divergence of the velocity minus a certain multiple of the pressure we find that f plays a crucial role in the entire analysis particularly in closing the required energy estimates understanding rates of regularization near the initial layer and most important obtaining time independent pointwise bounds for the density

quasiphantom categories on a family of surfaces isogenous to a higher product abstract we construct exceptional collections of line bundles of maximal length 4 on s c d g which is a surface isogenous to a higher product with p g q 0 where g g 32 27 is a finite group of order 32 having number 27 in the list of magma library from these exceptional collections we obtain new examples of quasiphantom categories as their orthogonal complements

tilt stability vanishing theorems and bogomolov gieseker type inequalities abstract we investigate the tilt stability of stable sheaves on projective varieties with respect to certain tilt stability conditions depends on two parameters constructed by bridgeland 11 see also 1 6 5 for a stable sheaf we give effective bounds of these parameters such that the stable sheaf is tilt stable these allow us to prove new vanishing theorems for stable sheaves and an effective serre vanishing theorem for torsion free sheaves using these results we also prove bogomolov gieseker type inequalities for the third chern character of a stable sheaf on p 3

mori dream stacks we propose a generalisation of mori dream spaces to stacks we show that this notion is preserved under root constructions and taking abelian gerbes unlike the case of mori dream spaces such a stack is not always given as a quotient of the spectrum of its cox ring by the picard group we give a criterion when this is true in terms of mori dream spaces and root constructions finally we compare this notion with that of smooth toric deligne mumford stacks

modelling age specific survival in nesting studies using a general approach for doubly censored and truncated data in typical nest survival studies the observed sample of nests is usually biased by left truncation i e only active nests enter the study additionally the failure data may be doubly censored because the exact dates of nest initiation and failure are uncertain we present a general bivariate contingency table approach for analyzing such data we use weakly structured step spline hazard models which avoid estimability problems encountered in a strictly nonparametric approach yet still permit flexibility our method eliminates a potential source of bias noted by heisey and nordheim 1990 biometrics 46 855 862 in the nest survival method of pollock and cornelius 1988 biometrics 44 397 404 we compare our approach to related techniques developed for estimating the incubation distribution of aids

global low energy weak solutions of the equations of three dimensional compressible magnetohydrodynamics we prove the global in time existence of weak solutions of the equations of compressible magnetohydrodynamics in three space dimensions with initial data small in l2 and initial density positive and essentially bounded a great deal of information concerning partial regularity is obtained velocity vorticity and magnetic field become relatively smooth in positive time h1 but not h2 and singularities in the pressure cancel those in a certain multiple of the divergence of the velocity thus giving concrete expression to conclusions obtained formally from the rankine hugoniot conditions

joint inference for competing risks survival data abstractthis article develops joint inferential methods for the cause specific hazard function and the cumulative incidence function of a specific type of failure to assess the effects of a variable on the time to the type of failure of interest in the presence of competing risks joint inference for the two functions are needed in practice because i they describe different characteristics of a given type of failure ii they do not uniquely determine each other and iii the effects of a variable on the two functions can be different and one often does not know which effects are to be expected we study both the group comparison problem and the regression problem we also discuss joint inference for other related functions our simulation shows that our joint tests can be considerably more powerful than the bonferroni method which has important practical implications to the analysis and design of clinical studies with competing risks data we illustrate our method using a hodgkin disease data and a

degree of the bicanonical map of a surface of general type let 5 be a smooth complex projective surface of general type rt 5 fpn l be the map defined by nks is called pluricanonical map for n 2 due to the works by bombieri and others in the 1970s the nature of n is determined except when n 2 and for some low values of invariants of 5 see 1 for an up to date treatment and references these maps play an important role in the classification of surfaces of general type recently the remaining case of the bicanonical map 2 for low values of invariants has aroused new research interests due to the work of francia 8 and especially the remarkable method of reider 15 see also 6 14 4 they have proved the following result among other things

the classification of double planes of general type with k2 8 and pg 0 abstract we study minimal double planes of general type with k 2 8 and p g 0 namely pairs s where s is a minimal complex algebraic surface of general type with k 2 8 and p g 0 and is an automorphism of s of order 2 such that the quotient s is a rational surface we prove that s is a free quotient f c g where c is a curve f is an hyperelliptic curve g is a finite group that acts faithfully on f and c and is induced by the automorphism id of f c being the hyperelliptic involution of f we describe all the f c and g that occur in this way we obtain 5 families of surfaces with p g 0 and k 2 8 of which we believe only one was previously known using our classification we are able to give an alternative description of these surfaces as double covers of the plane thus recovering a construction proposed by du val in addition we study the geometry of the subset of the moduli space of surfaces of general type with p g 0 and k 2 8 that admit a double plane structure

covariate analysis of competing risks data with log linear models a general system of log linear modeling is proposed for analysis of competing risks data with discrete covariates the instantaneous cause specific failure rates approximated by step functions are analyzed by techniques for multidimensional contingency tables censored observations are accommodated counts of failures of each type and the amount of follow up are summarized in two arrays in which each cell denotes a distinct combination of failure type time interval and covariate value maximum likelihood estimators for the parameters of the model are derived by iterative proportional fitting the resulting estimates of the number of failures in each cell are used for goodness of fit tests the principal advantages of this approach are its simple display of data its computational ease for the fitting and comparison of models and its provision of explicit goodness of fit tests interpretation of the models is facilitated by reference to several alternative models for survivorship and competing risks the basic model is extended to incorporate stochastic covariates whose values change during follow up and to accommodate quantitative covariates

log linear analysis of censored survival data with partially observed covariates abstract log linear models provide a flexible means of extending life table techniques for the analysis of censored survival data with categorical covariates as discussed by holford 1980 and laird and olivier 1981 we extend this methodology to incorporate cases in which one or more of the categorical covariates are sometimes missing maximum likelihood estimates of the parameters are calculated using data from all cases this can result in large gains in efficiency over standard methods that require the exclusion of cases with incomplete data with this approach we assume that the hazard function conditional on the covariates is a stepwise function over disjoint intervals of time the model has two parts a log linear model describing the hazard parameters and a multinomial model describing the probabilities in the contingency table defined by the covariates the main interest is in the model for the hazard parameters we show how to calculate maximum likelihood estimates of parameters of the mo

examples of smooth non general type surfaces in p4 smooth projective varieties with small invariants have received renewed interest in recent years primarily due to the fine study of the adjunction mapping now through the effort of several mathematicians a complete classification of smooth surfaces in bbb p 4 has been worked out up to degree 10 and a partial one is available in degree 11 on the other side recently ellingsrud and peskine have proved hartshorne s conjecture that there are only finitely many families of smooth surfaces in bbb p 4 not of general type it is believed that the degree of the smooth non general type surfaces in bbb p 4 should be less than or equal to 15 the aim of this paper is to provide a series of examples of smooth surfaces in bbb p 4 not of general type in degrees varying from 12 up to 14 and to describe their geometry by using mainly syzygies and liaison techniques we construct the following families of surfaces begin enumerate item minimal proper elliptic surfaces of degree 12 and sectional genus pi 13 item two types of non minimal proper elliptic surfaces of degree 12 and sectional genus pi 14 item non minimal k3 surfaces of degree 13 and sectional genus 16 and item non minimal k3 surfaces of degree 14 and sectional genus 19 1991 mathematics subject classification 14m07 14j25 14j26 14j28 14c05

derived categories of burniat surfaces and exceptional collections we construct an exceptional collection varupsilon of maximal possible length 6 on any of the burniat surfaces with k x 2 6 a 4 dimensional family of surfaces of general type with p g q 0 we also calculate the dg algebra of endomorphisms of this collection and show that the subcategory generated by this collection is the same for all burniat surfaces the semiorthogonal complement mathcal a of varupsilon is an almost phantom category it has trivial hochschild homology and k 0 mathcal a mathbb z 2 6

global existence in critical spaces for compressible navier stokes equations we investigate global strong solutions for isentropic compressible fluids with initial data close to a stable equilibrium we obtain the existence and uniqueness of a solution in a functional setting invariant by the scaling of the associated equations more precisely the initial velocity has the same critical regularity index as for the incompressible homogeneous navier stokes equations and one more derivative is needed for the density we point out a smoothing effect on the velocity and a l 1 decay on the difference between the density and the constant reference state the proof lies on uniform estimates for a mixed hyperbolic parabolic linear system with a convection term

unitary local systems multiplier ideals and polynomial periodicity of hodge numbers abstract the space of unitary local systems of rank one on the complement of an arbitrary divisor in a complex projective algebraic variety can be described in terms of parabolic line bundles we show that multiplier ideals provide natural stratifications of this space we prove a structure theorem for these stratifications in terms of complex tori and convex rational polytopes generalizing to the quasi projective case results of green lazarsfeld and simpson as an application we show the polynomial periodicity of hodge numbers h q 0 of congruence covers in any dimension generalizing results of e hironaka and sakuma we extend the structure theorem and polynomial periodicity to the setting of cohomology of unitary local systems in particular we obtain a generalization of the polynomial periodicity of betti numbers of unbranched congruence covers due to sarnak adams we derive a geometric characterization of finite abelian covers which recovers the classic one and the one of pardini we use this for example to prove a conjecture of libgober about hodge numbers of abelian covers

surfaces with pg q 3 we classify minimal complex surfaces of general type with p g q 3 more precisely we show that such a surface is either the symmetric product of a curve of genus 3 or a free z 2 quotient of the product of a curve of genus 2 and a curve of genus 3 our main tools are the generic vanishing theorems of green and lazarsfeld and the characterization of theta divisors given by hacon in corollary 3 4 of fourier transforms generic vanishing theorems and polarizations of abelian varieties

local structure of abelian covers abstract we study normal finite abelian covers of smooth varieties in particular we establish combinatorial conditions so that a normal finite abelian cover of a smooth variety is gorenstein or locally complete intersection

cohomological constraint on deformations of compact kahler manifolds abstract we prove that for every compact kahler manifold x the cup product h x t x h x x h x x 1 can be lifted to an l morphism from the kodaira spencer differential graded lie algebra to the suspension of the space of linear endomorphisms of the singular cohomology of x as a consequence we get an algebraic proof of the principle obstructions to deformations of compact kahler manifolds annihilate ambient cohomology

a simply connected numerical campedelli surface with an involution we construct a simply connected minimal complex surface of general type with p g 0 and k 2 2 which has an involution such that the minimal resolution of the quotient by the involution is a simply connected minimal complex surface of general type with p g 0 and k 2 1 in order to construct the example we combine a double covering and mathbb q gorenstein deformation especially we develop a method for proving unobstructedness for deformations of a singular surface by generalizing a result of burns and wahl which characterizes the space of first order deformations of a singular surface with only rational double points we describe the stable model in the sense of kollar and shepherd barron of the singular surfaces used for constructing the example we count the dimension of the invariant part of the deformation space of the example under the induced mathbb z 2 mathbb z action