Standard isotrivial fibrations with p_g=q=1

Abstract

A smooth, projective surface $S$ of general type is said to be a \emph{standard isotrivial fibration} if there exist a finite group $G$ which acts faithfully on two smooth projective curves $C$ and $F$ so that $S$ is isomorphic to the minimal desingularization of $T:=(C\times F)/G$. If $T$ is smooth then $S=T$ is called a $\text{quasi-bundle}$. In this paper we classify the standard isotrivial fibrations with $p_g=q=1$ 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 $p_g=q=1$ and $K_S^2=4,6$.

31 pages. Final version, to appear in J. Algebra

References in corpus (3)

• On surfaces of general type with p_g=q=1 isogenous to a product of curves
• The classification of surfaces with p_g = q = 0 isogenous to a product of curves
• Some (big) irreducible components of the moduli space of minimal surfaces of general type with $p_g=q=1$ and $K^2=4$

Cited by in corpus (9)

• Numerical properties of isotrivial fibrations
• On the Tate and Mumford-Tate conjectures in codimension one for varieties with h^{2,0}=1
• Standard isotrivial fibrations with p_g=q=1. II
• A family of surfaces with $p_g=q=2,K^2=7$ and Albanese map of degree $3$
• Topological types of actions on curves
• Algebraic Surfaces with $p_g=q=1,K^2=4$ and Genus 3 Albanese Fibration
• Isotrivially fibred surfaces and their numerical invariants
• On the minimal model of semi-isogenous mixed surfaces
• Algebraic Surfaces of General Type with $p_g=q=1$ and Genus 2 Albanese Fibrations