some koszul rings from geometry abstract we give examples of koszul rings that arise naturally in algebraic geometry in the first part we prove a general result on koszul property associated to an ample line bundle on a projective variety specifically we show how koszul property of multiples of a base point free ample line bundle depends on its castelnuovo mumford regularity in the second part we give examples of koszul rings that come from adjoint line bundles on minimal irregular surfaces of general type

dissipative boundary conditions for 2 2 hyperbolic systems of conservation laws for entropy solutions in bv in this article we investigate the bv stability of 2 2 hyperbolic systems of conservation laws with strictly positive velocities under dissipative boundary conditions more precisely we derive sufficient conditions guaranteeing the exponential stability of the system under consideration for entropy solutions in bv our proof is based on a front tracking algorithm used to construct approximate piecewise constants solutions whose bv norms are controlled through a lyapunov functional this lyapunov functional is inspired by the one proposed in j glimm s seminal work j glimm comm pure appl math 18 697 715 1965 modified with some suitable weights in the spirit of the previous works j m coron g bastin and b d andrea novel siam j control optim 47 3 1460 1498 2008 and j m coron b d andrea novel and g bastin ieee trans automat control 52 1 2 11 2007

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

a nadel vanishing theorem for metrics with minimal singularities on big line bundles abstract the purpose of this paper is to establish a nadel vanishing theorem for big line bundles with multiplier ideal sheaves of singular metrics admitting an analytic zariski decomposition such as metrics with minimal singularities and siu s metrics for this purpose we apply the theory of harmonic integrals and generalize enoki s proof of kollar s injectivity theorem moreover we investigate the asymptotic behavior of harmonic forms with respect to a family of regularized metrics

continuous dependence for 2 2 conservation laws with boundary on the domain 0 t x r t 0 and x 9 t for some boundary profile 9 r r as usual 1 1 is assumed to be strictly hyperbolic and with each characteristic field either linearly degenerate or genuinely non linear an initial data u 0 x u x having sufficiently small total variation is given we consider two different kinds of boundary conditions along x 9 t and in both cases we construct a lipschitzean flow whose trajectories are solutions of an initial boundary value problem for 1 1 thus we prove the continuous dependence of the solution upon the initial data upon the boundary condition and upon the boundary profile the existence theory for global bv solutions to the cauchy problem for 1 1 goes back to the fundamental paper 15 by glimm more recently in 6 a new approach has been introduced it relies on the construction of a lipschitzean semigroup the standard riemann semigroup srs whose trajectories extend the local standard lax 17 solutions of riemann problems at present such a srs has been constructed in the 2 2 case in 8 9 while for the general n n case see 7 10 and 3 in article no de973274

on general balance laws with boundary this paper is devoted to general balance laws with a possibly non local source term with a non characteristic boundary basic well posedness results are obtained trying to provide sharp estimates in particular bounds tend to blow up as the boundary tends to be characteristic new uniqueness results for the solutions to conservation and or balance laws with boundary are also provided

a modified kahler ricci flow in this note we study a kahler ricci flow modified from the classic version in the non degenerate case strong convergence at infinite time is achieved the main focus should be on degenerate case where some partial results are presented

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

mixed systems odes balance laws abstract we prove the well posedness of mixed problems consisting of a system of ordinary differential equations coupled with systems of balance laws in domains with moving boundaries the interfaces between the systems are provided by the boundary data and boundary positions various situations that fit into this framework are studied both analytically and numerically we consider a piston moving in a pipe full of fluid a model for fluid particle interaction and a traffic model references to other examples in the literature are provided

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

relative critical exponents non vanishing and metrics with minimal singularities in this article we establish a very general non vanishing statement as well as several properties of metrics with minimal singularities of adjoint bundles our arguments combine the proof of the classical non vanishing theorem due to v shokurov as well as many ideas from y t siu s analytic proof of the finite generation of the canonical ring an important tool is the notion of relative critical exponent of two closed positive currents with respect to a measure

on the stability functional for conservation laws this note is devoted to the explicit construction of a functional defined on all pairs of l 1 functions with small total variation which is equivalent to the l 1 distance and non increasing along the trajectories of a given system of conservation laws the present definition of this functional does not need any construction of approximate solutions

automorphisms of finite order on gorenstein del pezzo surfaces in this paper we shall determine all actions of groups of prime order p with p 5 on gorenstein del pezzo singular surfaces y of picard number 1 we show that every order p element in aut y aut y y being the minimal resolution of y is lifted from a projective transformation of p 2 we also determine when aut y is finite in terms of k 2 y sing y and the number of singular members in k in particular we show that either aut y 2 a 3 b for some 1 5 there is at least one element gp of order p in aut y hence aut y is infinite

on the abundance theorem in the case of numerical kodaira dimension zero we present a shorter proof of the abundance theorem in the case of numerical kodaira dimension 0 proved by nakayama and its log generalization

generalizations of siegel s and picard s theorems we prove new theorems that are higher dimensional generalizations of the classical theorems of siegel on integral points on affine curves and of picard on holomorphic maps from c to affine curves these include results on integral points over varying number fields of bounded degree and results on kobayashi hyperbolicity we give a number of new conjectures describing from our point of view how we expect siegel s and picard s theorems to optimally generalize to higher dimensions in this article we prove new theorems that are higher dimensional generaliza tions of the classical theorems of siegel on integral points on affine curves and of picard on holomorphic maps from c to affine curves in section 2 we will give the statements of siegel s and picard s theorems and we will recall how these two theorems from such seemingly different areas of mathematics are related we will then proceed to give a number of new conjectures describing from our point of view how we expect siegel s and picard s theorems to optimally generalize to higher dimensions these include conjectures on integral points over varying number fields of bounded degree and conjectures addressing hyperbolic questions these conjectures appear to be fundamentally new we will then summarize our progress on these conjectures we have been able to get results in all dimensions with best possible results in many cases for surfaces

a parallel algorithm for solving the inverse scattering moment problem abstract a plane incident wave impinges upon an unknown acoustically soft scatterer it is assumed that the scatterer has a polynomial boundary it is star shaped and its characteristic dimension is much less than the wavelength of the incident field an analytic procedure is proposed to reduce the shape reconstruction process to the evaluation of certain expansion coefficients and the solution of a linear algebraic system then a parallel numerical algorithm is constructed which recovers the exact shape of the scatterer from the knowledge of a finite number of generalized low frequency moments generated by the leading low frequency approximation the efficiency of the proposed algorithm as well as the detailed parametric influence on the performance of the algorithm are extensively investigated

on the logarithmic plurigenera of complements of plane curves let b be a not necessarily irreducible plane curve in 2 in the present article we prove that if and only if moreover we determine the curve b when and

f singularities via alterations we give characterizations of test ideals and f rational singularities via regular alterations formally the descriptions are analogous to standard characterizations of multiplier ideals and rational singularities in characteristic zero via log resolutions lastly we establish nadel type vanishing theorems up to finite maps for test ideals and further demonstrate how these vanishing theorems may be used to extend sections

a nadel vanishing theorem via injectivity theorems the purpose of this paper is to establish nadel type vanishing theorems with multiplier ideal sheaves of singular metrics admitting an analytic zariski decomposition such as metrics with minimal singularities and siu s metrics for this purpose we generalize kollar s injectivity theorem to an injectivity theorem for line bundles equipped with singular metrics by making use of the theory of harmonic integrals moreover we give asymptotic cohomology vanishing theorems for high tensor powers of line bundles

a matroid invariant via the k theory of the grassmannian abstract let g d n denote the grassmannian of d planes in c n and let t be the torus c n diag c which acts on g d n let x be a point of g d n and let t x be the closure of the t orbit through x then the class of the structure sheaf of t x in the k theory of g d n depends only on which plucker coordinates of x are nonzero combinatorial data known as the matroid of x in this paper we will define a certain map of additive groups from k g d n to z t letting g x t denote the image of 1 n dim t x o t x g x behaves nicely under the standard constructions of matroid theory such as direct sum two sum duality and series and parallel extensions we use this invariant to prove bounds on the complexity of kapranov s lie complexes m kapranov chow quotients of grassmannians i adv soviet math 16 2 1993 29 110 hacking keel and tevelev s very stable pairs p hacking s keel e tevelev compactification of the moduli space of hyperplane arrangements j algebraic geom 15 2006 657 680 and the author s tropical linear spaces when they are realizable in characteristic zero d speyer tropical linear spaces siam j discrete math 22 4 2008 1527 1558 namely in characteristic zero a lie complex or the underlying d 1 dimensional scheme of a very stable pair can have at most n i 1 d i n d i i 1 strata of dimensions n i and d i respectively this prove the author s f vector conjecture from d speyer tropical linear spaces siam j discrete math 22 4 2008 1527 1558 in the case of a tropical linear space realizable in characteristic 0

boundary conditions for nonlinear hyperbolic systems of conservation laws we propose two formulations of the boundary conditions for nonlinear hyperbolic systems of conservation laws a first approach is based on the vanishing viscosity method and a second one is related to the riemann problem the equivalence between these two conditions is studied the latter formulation is extended to treat numerically physically relevant boundary conditions monodimensional experiments are presented

weights on cohomology invariants of singularities and dual complexes we study the weight filtration on the cohomology of a proper complex algebraic variety and obtain natural upper bounds on its size when it is the exceptional divisor of a singularity we also give bounds for the cohomology of links the invariants of singularities introduced here gives rather strong information about the topology of rational and related singularities