the absolute galois group acts faithfully on regular dessins and on beauville surfaces in this article we study the action of the absolute galois group gal q q on dessins d enfants and beauville surfaces a foundational result in grothendieck s theory of dessins d enfants is the fact that the absolute galois group gal q q acts faithfully on the set of all dessins however the question of whether this holds true when the action is restricted to the set of the more accessible regular dessins seems to be still an open question in the first part of this paper we give an affirmative answer to it in fact we prove the strongest result that the action is faithful on the set of quasiplatonic or triangle curves of any given hyperbolic type beauville surfaces are an important kind of algebraic surfaces introduced by catanese they are rigid surfaces of general type closely related to dessins d enfants here we prove that for any gal q q different from the identity and the complex conjugation there is a beauville surface s such that s and its galois conjugate s have non isomorphic fundamental groups this in turn easily implies that the action of gal q q on the set of beauville surfaces is faithful these results were conjectured by bauer catanese and grunewald and immediately imply that gal q q acts faithfully on the connected components of the moduli space of surfaces of general type a result due to the above mentioned authors

calculation of a constant q spectral transform the frequencies that have been chosen to make up the scale of western music are geometrically spaced thus the discrete fourier transform dft although extremely efficient in the fast fourier transform implementation yields components which do not map efficiently to musical frequencies this is because the frequency components calculated with the dft are separated by a constant frequency difference and with a constant resolution a calculation similar to a discrete fourier transform but with a constant ratio of center frequency to resolution has been made this is a constant q transform and is equivalent to a 1 24 oct filter bank thus there are two frequency components for each musical note so that two adjacent notes in the musical scale played simultaneously can be resolved anywhere in the musical frequency range this transform against log frequency to obtain a constant pattern in the frequency domain for sounds with harmonic frequency components has been plotted this is compared to the conventio

q e d for algebraic varieties we introduce a new equivalence relation for complete algebraic varieties with canonical singularities generated by birational equivalence by flat algebraic deformations of varieties with canonical singularities and by quasi etale morphisms i e morphisms which are unramified in codimension 1 we denote the above equivalence by a q e d algebraic quasi etale deformation a completely similar equivalence relation denoted by c q e d can be considered for compact complex spaces with canonical singularities by a recent theorem of siu dimension and kodaira dimension are invariants for a q e d of complex varieties we address the interesting question whether conversely two algebraic varieties of the same dimension and with the same kodaira dimension are q e d equivalent a q e d or at least c q e d the answer being positive for curves by well known results using enriques resp kodaira s classification we show first that the answer to the c q e d question is positive for special algebraic surfaces those with kodaira dimension at most 1 resp for compact complex surfaces with kodaira dimension 0 1 and even first betti number

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

examples of summing integral and nuclear operators on the space c 0 1 x with values in c0 abstract we give necessary and sufficient conditions that some operators on the space c 0 1 x with values in c 0 be as in the title related questions are investigated

the least squares invertible constant q spectrogram and its application to phase vocoding this paper discusses the development of a constant q spectrogram representation that is invertible in a least squares sense a good quality inverse is possible because this modified transform method unlike the usual sliding window constant q spectrogram does not discard data samples when performing the variable length discrete fourier transforms on the signal the development of a phase vocoder application using this modified technique is also discussed it is shown that a phase vocoder constructed using the least squares invertible constant q spectrogram lsicqs is not a trivial extension of the regular fft based phase vocoder algorithm and some of the mathematical subtleties related to phase reassignment are addressed

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

non homeomorphic galois conjugate beauville structures on psl 2 p abstract catanese s rigidity results for surfaces isogenous to a product of curves indicate that beauville surfaces should provide a fertile source of examples of galois conjugate varieties that are not homeomorphic a phenomenon discovered by j p serre in the sixties in this paper we construct beauville surfaces s c 1 c 2 g with group g psl 2 p for p 7 and curves c 1 c 2 such that the orbit of s under the action of the absolute galois group gal q q contains non homeomorphic conjugate surfaces when p 7 the orbit consists exactly of two surfaces that have non isomorphic fundamental groups and the curves c 1 c 2 have genera 8 and 49 which is shown to be the minimum for which there is a pair of non homeomorphic galois conjugate beauville surfaces as p grows the orbits contain an arbitrarily large number of non homeomorphic surfaces along the way we prove a metric rigidity theorem for beauville surfaces which provides an elementary proof of the part of catanese s theory needed to prove our results

on beauville structures on the groups sn and an it is known that the symmetric group s n for n 5 and the alternating group a n for large n admit a beauville structure in this paper we prove that a n admits a beauville resp strongly real beauville structure if and only if n 6 resp n 7 we also show that s n admits a strongly real beauville structure for n 5

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

effective invariants of braid monodromy in this paper we construct new invariants of algebraic curves based on not necessarily generic braid monodromies such invariants are effective in the sense that their computation allows for the study of zariski pairs of plane curves moreover the zariski pairs found in this work correspond to curves having conjugate equations in a number field and hence are not distinguishable by means of computing algebraic coverings we prove that the embeddings of the curves in the plane are not homeomorphic we also apply these results to the classification problem of elliptic surfaces

fuchsian triangle groups and grothendieck dessins variations on a theme of belyi according to a theorem of belyi a smooth projective algebraic curve is defined over a number field if and only if there exists a non constant element of its function field ramified only over 0 1 and the existence of such a belyi function is equivalent to that of a representation of the curve as a possibly compactified quotient space of the poincare upper half plane by a subgroup of finite index in a fuchsian triangle group on the other hand fuchsian triangle groups arise in many contexts such as in the theory of hypergeometric functions and certain triangular billiard problems which would appear at first sight to have no relation to the galois problems that motivated the above discovery of belyi in this note we review several results related to belyi s theorem and we develop certain aspects giving examples for preliminary accounts see the preprint wo1 the conference proceedings article bauitz and the comptes rendus note cowo2

fibred surfaces varieties isogenous to a product and related moduli spaces a fibration of an algebraic surface s over a curve b with fibres of genus at least 2 has constant moduli iff it is birational to the quotient of a product of curves by the action of a finite group g a variety isogenous to a higher product is the quotient of a product of curves of genus at least 2 by the free action of a finite group theorem b gives a characterization of surfaces isogenous to a higher product in terms of the fundamental group and of the euler number theorem c classifies the groups thus occurring and shows that after fixing the group and the euler number one obtains an irreducible moduli space the result of theorem b is extended to higher dimension in theorem g thus generalizing cf also theorem h results of jost yau and mok concerning varieties whose universal cover is a polydisk theorem a shows that fibrations where the fibre genus and the genus of the base b are at least 2 are invariants of the oriented differentiable structure the main theorems d and e characterize surfaces carrying constant moduli fibrations as surfaces having a zariski open set satisfying certain topological conditions e g having the right euler number the right fundamental group and the right fundamental group at infinity 0 introduction the study of fibrations of a smooth algebraic surface s over a smooth algebraic curve b lies at the heart of the classification theory and of the geometry of algebraic surfaces our main results in this paper theo rems d e concern a topological characterization of surfaces admitting a constant moduli fibration these results are intimately related to a series of variations on the same theme also in higher dimension and to a circle of allied techniques which we present in the course of the paper the first new result we have in this direction and which is presented in section 2 after we recall several known results some classical some quite recent is the following theorem on the dif ferentiable invariance of the genus of fibres cf theorem 2 9 for a more precise statement theorem a let f s b be a fibration of the surface s over a curve b of genus b 2 and with fibre f of genus g 1 assume that s is another smooth compact kahler surface which is orientedly diffeomorphic to s then the subspace of h 1 s corresponding to f h 1 b determines a fibration f s b with

faithful actions of the absolute galois group on connected components of moduli spaces we use a canonical procedure associating to an algebraic number a first a hyperelliptic curve c a and then a triangle curve d a g a obtained through the normal closure of an associated belyi function in this way we show that the absolute galois group mathrm gal bar mathbb q mathbb q acts faithfully on the set of isomorphism classes of marked triangle curves and on the set of connected components of marked moduli spaces of surfaces isogenous to a higher product these are the free quotients of a product c 1 times c 2 of curves of respective genera g 1 g 2 ge 2 by the action of a finite group g we show then using again the surfaces isogenous to a product first that it acts faithfully on the set of connected components of the moduli space of surfaces of general type amending an incorrect proof in a previous arxiv version of the paper and then as a consequence we obtain our main result for each element sigma in mathrm gal bar mathbb q mathbb q not in the conjugacy class of complex conjugation there exists a surface of general type x such that x and the galois conjugate surface x sigma have nonisomorphic fundamental groups using polynomials with only two critical values we can moreover exhibit infinitely many explicit examples of such a situation

2 absolutely summing operators on the space c t x abstract we give for some banach spaces x and y examples of linear and continuous operators u c t x y such that u as2 x y for each c t and u c t as2 x y is a 2 absolutely summing operator with respect to the 2 absolute norm on as2 x y but u is not 2 absolutely summing

operator valued operators that are associated to vector valued operators this paper is motivated by a long standing conjecture of dinculeanu from 1967 let x and y be banach spaces and let be a compact hausdorff space dinculeanu conjectured that there exist operators s l c l x y s l c l x y which are not associated to any u l c x y u l c x y we study this existence problem systematically on three possible levels of generality the classical case c x c x of continuous vector valued functions p continuous vector valued functions and tensor products on each level we establish necessary and sufficient conditions for an l x y l x y valued operator to be associated to a y valued operator among others we see that examples proving dinculeanu s conjecture come out on the all three levels of generality

on α nuclear operators with applications to vector valued function spaces abstract let x be a banach space and let y be a closed subspace of a banach space z let be a tensor norm our main result is as follows assume that x or z has the approximation property if there is a bounded linear extension operator from y to z then any bounded linear operator t x y is nuclear whenever t is nuclear from x to z using this result we characterize the space c p x respectively uc p x of continuous functions from a compact hausdorff space into a banach space x whose range is p compact respectively unconditionally p compact

some remarks on the universal cover of an open k3 surface we shall give in an optimal form a sufficient numerical condition for the finiteness of the fundamental group of the smooth locus of a normal k3 surface we shall moreover prove that if the normal k3 surface is elliptic and the above fundamental group is not finite then there is a finite covering which is a complex torus

nonhomeomorphic conjugates of connected shimura varieties we show that conjugation by an automorphism of bbb c may change the topological fundamental group of a locally symmetric variety over bbb c as a consequence we obtain a large class of algebraic varieties defined over number fields with the property that different embeddings of the number field into bbb c give complex varieties with nonisomorphic fundamental groups

an efficient algorithm for the calculation of a constant q transform an efficient method of transforming a discrete fourier transform dft into a constant q transform where q is the ratio of center frequency to bandwidth has been devised this method involves the calculation of kernels that are then applied to each subsequent dft only a few multiples are involved in the calculation of each component of the constant q transform so this transformation adds a small amount to the computation in effect this method makes it possible to take full advantage of the computational efficiency of the fast fourier transform fft graphical examples of the application of this calculation to musical signals are given for sounds produced by a clarinet and a violin

the bartle dunford schwartz and the dinculeanu singer theorems revisited abstract let x and y be banach spaces and let be a compact hausdorff space by the classical bartle dunford schwartz theorem any operator s l c y admits an integral representation with respect to a y valued measure by the dinculeanu singer theorem each operator u l c x y admits an integral representation with respect to an l x y valued measure we establish an integral representation for any operator s l c l x y with respect to an l x y valued measure this far reaching extension of the bartle dunford schwartz theorem serves as a departure point for a general integral representation theory developed in the present paper in particular it is an efficient tool that enables us to give an alternative simple proof to the dinculeanu singer theorem the latter theorem is proved in a more general context of x valued continuous functions with p compact range among others useful formulas which connect different vector measures are deduced

fibered stable varieties reference epfl article 231103doi 10 1090 tran 6386 url http dx doi org 10 1090 tran 6386 record created on 2017 09 19 modified on 2017 10 02

hurwitz equivalence of braid monodromies and extremal elliptic surfaces we discuss the equivalence between the categories of certain ribbon graphs and subgroups of the modular group and use this equivalence to construct exponentially large families of not hurwitz equivalent simple braid monodromy factorizations of the same element as an application we also obtain exponentially large families of topologically distinct algebraic objects such as extremal elliptic surfaces real trigonal curves and real elliptic surfaces

beauville surfaces and finite groups abstract extending results of bauer catanese and grunewald and of fuertes and gonzalez diez we show that beauville surfaces of unmixed type can be obtained from the groups l 2 q and sl 2 q for all prime powers q 5 and the suzuki groups sz 2 e and the ree groups r 3 e for all odd e 3 we also show that l 2 q and sl 2 q admit strongly real beauville structures yielding real beauville surfaces for all q 5

green forms and the arithmetic siegel weil formula we construct natural green forms for special cycles in orthogonal and unitary shimura varieties in all codimensions and for compact shimura varieties of type mathrm o p 2 and mathrm u p 1 we show that the resulting local archimedean height pairings are related to special values of derivatives of siegel eisentein series a conjecture put forward by kudla relates these derivatives to arithmetic intersections of special cycles and our results settle the part of his conjecture involving local archimedean heights

deformation theory generic vanishing theorems and some conjectures of enriques catanese and beauville introduction 389 w notation and conventions 392 w deformations of cohomology groups 392 w generic vanishing criteria for topologically trivial line bundles 397 w a nakano type generic vanishing theorem 401 w an application to surfaces 405 references 407

belyi s theorem for complex surfaces belyi s theorem states that a compact riemann surface c can be defined over a number field if and only if there is on it a meromorphic function f with three critical values such functions resp riemann surfaces are called belyi functions resp belyi surfaces alternatively belyi surfaces can be characterized as those which contain a proper zariski open subset uniformised by a torsion free subgroup of the classical modular group sl2 z in this article we establish a result analogous to belyi s theorem in complex dimension two it turns out that the role of belyi functions is now played by composed lefschetz pencils with three critical values while the analogous to torsion free subgroups of the modular group will be certain extensions of them acting on a bergmann domain of 2 these groups were first introduced by bers and griffiths

examples of mori dream surfaces of general type with pg 0 abstract in this paper we study effective nef and semiample cones of minimal surfaces of general type with p g 0 we provide examples of minimal surfaces of general type with p g 0 and 2 k 2 9 which are mori dream spaces on these examples we also give explicit description of their effective cones with all negative curves we also present non minimal surfaces of general type with p g 0 that are not mori dream surfaces

generation of finite quasisimple groups with an application to groups acting on beauville surfaces we verify a conjecture of bauer catanese and grunewald by proving a stronger result concerning quasisimple groups more specifically we prove that every finite quasisimple group apart from a5 and its cover sl 2 5 is a beauville group

beauville structures in finite p groups abstract we study the existence of unmixed beauville structures in finite p groups where p is a prime first of all we extend catanese s characterisation of abelian beauville groups to finite p groups satisfying certain conditions which are much weaker than commutativity this result applies to all known families of p groups with a good behaviour with respect to powers regular p groups powerful p groups and more generally potent p groups and generalised p central p groups in particular our characterisation holds for all p groups of order at most p p which allows us to determine the exact number of beauville groups of order p 5 for p 5 and of order p 6 for p 7 on the other hand we determine which quotients of the nottingham group over f p are beauville groups for an odd prime p as a consequence we give the first explicit infinite family of beauville 3 groups and we show that there are beauville 3 groups of order 3 n for every n 5

invariants of plane algebraic curves via representations of the braid groups recently new remarkable polynomial invariants of knots in 3 sphere were introduced using some representations of the braid groups which were shown to be effective in distinguishing knots j fyhlmo the purpose of this note is to introduce using representation of the braid groups an invariant of continuous equisingular families of plane algebraic curves a pleasant feature is that this invariant is defined for any representation of the braid group no coherence of representations for different number of strings is required though for many representations this invariant is trivial in the case of the reduced burau representation this invariant essentially coincides with the alexander polynomial of plane curves introduced in l 1 this fact is the counterpart of the well known relation between the alexander polynomial of closed braids and the reduced burau representation the definition of this invariant depends on braid monodromy associated with the curve m in particular we obtain a direct not involving calculations of the fundamental group though computationally cumbersome method of computation of the alexander polynomial via braid monodromy in the next section we shall recall the background on continuous equisingular families of plane algebraic curves and their braid monodromies in the sect 3 we introduce the invariant and in the last section we consider the case of reduced burau representations

on extendability of group actions on compact riemann surfaces the question of whether a given group g which acts faithfully on a compact riemann surface x of genus g 2 is the full group of automorphisms of x or some other such surface of the same genus is considered conditions are derived for the extendability of the action of the group g in terms of a concrete partial presentation for g associated with the relevant branching data using singerman s list of signatures of fuchsian groups that are not finitely maximal by way of illustration the results are applied to the special case where g is a non cyclic abelian group

p summing operators on injective tensor products of spaces the final version of this paper appears in proceedings of the royal society of edinburgh section b 120a 1992 283 296 print

braid monodromy and topology of plane curves in this paper we prove that braid monodromy of an affine plane curve determines the topology of a related projective plane curve

localization of the complex spectrum the s transform the s transform which is introduced in the present correspondence is an extension of the ideas of the continuous wavelet transform cwt and is based on a moving and scalable localizing gaussian window it is shown to have some desirable characteristics that are absent in the continuous wavelet transform the s transform is unique in that it provides frequency dependent resolution while maintaining a direct relationship with the fourier spectrum these advantages of the s transform are due to the fact that the modulating sinusoids are fixed with respect to the time axis whereas the localizing scalable gaussian window dilates and translates