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Matteo Penegini

Publications and source records attributed to Matteo Penegini.

28 records · Page 2Linked to original sources
arXiv2014

A new family of surfaces with $p_g=q=2$ and $K^2=6$ whose Albanese map has degree $4$

We construct a new family of minimal surfaces of general type with $p_g=q=2$ and $K^2=6$, 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 $p_g=q=2$ and $K^2=6$. Finally, we prove that such a component is generically smooth of dimension 4 and that it contains the 2-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 $\mathscr{H}_3$.

math.AG↗
arXiv2013

Surfaces isogenous to a product of curves, braid groups and mapping class groups

This article is a revised version of the talk I gave at the conference ``Beauville Surfaces and groups'' held in Newcastle in June 2012. It presents some group theoretical methods to give bounds on the number of connected components of the moduli space of surfaces of general type, focusing on some families of regular surfaces isogenous to a product of curves.

math.AG↗
arXiv2013

On the classification of surfaces of general type with $p_g=q=2$

The paper is an extended version of the talk which I gave at the XIX Congresso dell'UMI in Bologna in September 2011. The aim of this paper is twofold: first, to give an overview on the recent development in the classification of surfaces of general type with $p_g=q=2$; second, to point out some of the problems that are still open.

math.AG↗
arXiv2013

K3 surfaces with a non-symplectic automorphism and product-quotient surfaces with cyclic groups

We classify all the K3 surfaces which are minimal models of the quotient of the product of two curves $C_1\times C_2$ by the diagonal action of either the group $\Z/p\Z$ or the group $\Z/2p\Z$. These K3 surfaces admit a non-symplectic automorphism of order $p$ induced by an automorphism of one of the curves $C_1$ or $C_2$. We prove that most of the K3 surfaces admitting a non-symplectic automorphism of order $p$ (and in fact a maximal irreducible component of the moduli space of K3 surfaces with a non-symplectic automorphism of order $p$) are obtained in this way.\\ In addition, we show that one can obtain the same set of K3 surfaces under more restrictive assumptions namely one of the two curves, say $C_2$, is isomorphic to a rigid hyperelliptic curve with an automorphism $δ_p$ of order $p$ and the automorphism of the K3 surface is induced by $δ_p$.\\ Finally, we describe the variation of the Hodge structures of the surfaces constructed and we give an equation for some of them.

math.AG↗
arXiv2012

New Beauville surfaces and finite simple groups

In this paper we construct new Beauville surfaces with group either $\PSL(2,p^e)$, or belonging to some other families of finite simple groups of Lie type of low Lie rank, or an alternating group, or a symmetric group, proving a conjecture of Bauer, Catanese and Grunewald. The proofs rely on probabilistic group theoretical results of Liebeck and Shalev, on classical results of Macbeath and on recent results of Marion.

math.GR↗
arXiv2012

On surfaces with p_g=q=2, K^2=5 and Albanese map of degree 3

We construct a connected, irreducible component of the moduli space of minimal surfaces of general type with $p_g=q=2$ and $K^2=5$, 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.

math.AG↗
arXiv2012

Surfaces with p_g=q=2, K^2=6 and Albanese map of degree 2

We classify minimal surfaces $S$ of general type with $p_g=q=2$ and $K_S^2=6$ whose Albanese map is a generically finite double cover. We show that the corresponding moduli space is the disjoint union of three generically smooth, irreducible components $\mathcal{M}_{Ia}$, $\mathcal{M}_{Ib}$, $\mathcal{M}_{II}$ of dimension 4, 4, 3, respectively. The general surface $S$ contains a smooth elliptic curve $Z$ such that $Z^2=-2$, which is contracted by the Albanese map and which is preserved by any first-order deformation.

math.AG↗
arXiv2011

Beauville surfaces, moduli spaces and finite groups

In this paper we give the asymptotic growth of the number of connected components of the moduli space of surfaces of general type corresponding to certain families of Beauville surfaces with group either $\PSL(2,p)$, or an alternating group, or a symmetric group or an abelian group. We moreover extend these results to regular surfaces isogenous to a higher product of curves.

math.AG↗
arXiv2010

The classification of isotrivially fibred surfaces with p_g=q=2

An isotrivially fibred surface is a smooth projective surface endowed with a morphism onto a curve such that all the smooth fibres are isomorphic to each other. The first goal of this paper is to classify the isotrivially fibred surfaces with $p_g=q=2$ completing and extending a result of Zucconi. As an important byproduct, we provide new examples of minimal surfaces of general type with $p_g=q=2$ and $K^2=4,5$ and a first example with $K^2=6$.

math.AG↗