Standard isotrivial fibrations with p_g=q=1. II

Abstract

A smooth, projective surface $S$ is called a $\text{standard isotrivial fibration}$ if there exists 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 $T:=(C\times F)/G$. Standard isotrivial fibrations of general type with $p_g=q=1$ have been classified in \cite{Pol07} under the assumption that $T$ has only Rational Double Points as singularities. In the present paper we extend this result, classifying all cases where $S$ is a minimal model. As a by-product, we provide the first examples of minimal surfaces of general type with $p_g=q=1$, $K_S^2=5$ and Albanese fibration of genus 3. Finally, we show with explicit examples that the case where $S$ is not minimal actually occurs.

32 pages. Final version, to appear in the Journal of Pure and Applied Algebra

References in corpus (2)

• Standard isotrivial fibrations with p_g=q=1
• The classification of surfaces with p_g=q=1 isogenous to a product of curves

Cited by in corpus (2)

• Numerical properties of isotrivial fibrations
• Topological types of actions on curves