Standard isotrivial fibrations with p_g=q=1. II

Ernesto Mistretta; Francesco Polizzi

doi:10.1016/j.jpaa.2009.05.010

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arXiv · 0805.1424

Standard isotrivial fibrations with p_g=q=1. II

Ernesto Mistretta·Francesco Polizzi

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Abstract

A smooth, projective surface $S$ is called a $\emph{standard isotrivial fibration}$ 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.

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Ernesto Mistretta, Francesco Polizzi. 2009-05-27. Standard isotrivial fibrations with p_g=q=1. II. https://doi.org/10.1016/j.jpaa.2009.05.010

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