1,720,995 research outputs found
Monodromy representations and surfaces with maximal Albanese dimension
Full text linkWe relate the existence of some surfaces of general type and maximal Albanese dimension to the existence of some monodromy representations of the braid group B2(C2) in the symmetric group Sn. Furthermore, we compute the number of such representations up to n= 9 , and we analyze the cases n∈{2,3,4}. For n=2,3 we recover some surfaces with pg= q= 2 recently studied (with different methods) by the author and his collaborators, whereas for n= 4 we obtain some conjecturally new examples
On surfaces with pg = q = 2, k2 = 5 and albanese map of degree 3
No full textWe construct a connected, irreducible component of the moduli space of minimal surfaces of general type with pg = q = 2 and K2 = 5, which contains both examples given by Chen-Hacon and the first author. This component is generically smooth of dimension 4, and all its points parametrize surfaces whose Albanese map is a generically finite triple cover
A new family of surfaces with pg = q = 2 and K2 = 6 whose Albanese map has degree 4
Full text linkWe construct a new family of minimal surfaces of general type with pg = q = 2 and K2 = 6, whose Albanese map is a quadruple cover of an abelian surface with polarization of type (1, 3). We also show that this family provides an irreducible component of the moduli space of surfaces with pg = q = 2 and K2 = 6. Finally, we prove that such a component is generically smooth of dimension 4 and that it contains the two-dimensional family of product-quotient examples previously constructed by the first author. The main tools we use are the Fourier-Mukai transform and the Schrödinger representation of the finite Heisenberg group H3
Representations of braid groups and construction of projective surfaces
Full text linkBraid groups are an important and flexible tool used in several areas of science, such as Knot Theory (Alexander's theorem), Mathematical Physics (Yang-Baxter's equation) and Algebraic Geometry (monodromy invariants). In this note we will focus on their algebraic-geometric aspects, explaining how the representation theory of higher genus braid groups can be used to produce interesting examples of projective surfaces defined over the field of complex numbers
Surfaces of general type with pg = q = 1, K2 = 8 and bicanonical map of degree 2
Full text linkWe classify the minimal algebraic surfaces of general type with p g = q = 1, K2 = 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 × F such that S = (C × 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 φ of S is composed with the involution a induced on S by τ × id: C × F → C × F, where τ is the hyperelliptic involution of C. In this way we obtain three families of surfaces with pg = q = 1, K2 = 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 pg = 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. © 2005 American Mathematical Society
Numerical properties of isotrivial fibrations
Full text linkIn this paper we investigate the numerical properties of relatively minimal isotrivial fibrations φ: X → C, where X is a smooth, projective surface and C is a curve. In particular we prove that, if g(C) ≥ 1 and X is neither ruled nor isomorphic to a quasi-bundle, then; this inequality is sharp and if equality holds then X is a minimal surface of general type whose canonical model has precisely two ordinary double points as singularities. Under the further assumption that KX is ample, we obtain and the inequality is also sharp. This improves previous results of Serrano and Tan. © 2010 Springer Science+Business Media B.V
On surfaces of general type with pg = q = 1 isogenous to a product of curves
Full text linkA smooth algebraic surface S is said to be isogenous to a product of unmixed type if there exist two smooth curves C, F and a finite group G, acting faithfully on both C and F and freely on their product, so that S = (C x F)/G. In this article, we classify the surfaces of general type with pg = q = 1 which are isogenous to an unmixed product, assuming that the group G is abelian. It turns out that they belong to four families, that we call surfaces of type I, II, III, IV. The moduli spaces RI, RII, RIV are irreducible, whereas RIII is the disjoint union of two irreducible components. In the last section we start the analysis of the case where G is not abelian, by constructing several examples. Copyright © Taylor & Francis Group, LLC
Surface braid groups, finite Heisenberg covers and double Kodaira fibrations
Full text linkWe exhibit new examples of double Kodaira fibrations using finite Galois covers of a product Σb x Σb, where 6b is a smooth projective curve of genus b " 2. Each cover is obtained by providing an explicit group epimorphism from the pure braid group P2(6b) to some finite Heisenberg group. In this way, we are able to show that every curve of genus b is the base of a double Kodaira fibration; moreover, the number of pairwise non-isomorphic Kodaira fibred surfaces fibering over a fixed curve 6b is at least ω(b + 1), where ω: N → N stands for the arithmetic function counting the number of distinct prime factors of a positive integer. As a particular case of our general construction, we obtain a real 4-manifold of signature 144 that can be realized as a real surface bundle over a surface of genus 2, with fibre genus 325, in two different ways. This provides (to our knowledge) the first "double solution" to a problem from Kirby's problem list in low-dimensional topology
Diagonal double Kodaira structures on finite groups
Full text linkWe introduce some special presentations on finite groups, that we call
"diagonal double Kodaira structures" and whose existence is equivalent to the
existence of some special Kodaira fibred surfaces, that we call "diagonal
double Kodaira fibrations". This allows us to rephrase in purely algebraic
terms some results about finite Heisenberg groups, previously obtained in the
recent work of the author with A. Causin, and makes possible to extend them to
the case of arbitrary extra-special -groups.Comment: To appear in the Proceedings of the 2019 ISAAC Congress (Aveiro,
Portugal
Standard isotrivial fibrations with pg=q=1
Full text linkAbstractA smooth, projective surface S of general type is said to be a standard isotrivial fibration if there exists a finite group G acting faithfully on two smooth projective curves C and F so that S is isomorphic to the minimal desingularization of T:=(C×F)/G. If T is smooth then S=T is called a quasi-bundle. In this paper we classify the standard isotrivial fibrations with pg=q=1 which are not quasi-bundles, assuming that all the singularities of T are rational double points. As a by-product, we provide several new examples of minimal surfaces of general type with pg=q=1 and KS2=4,6
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