Standard isotrivial fibrations with p_g=q=1

Details Standard isotrivial fibrations with p_g=q=1 Standard isotrivial fibrations with p_g=q=1

2007-03-02

arxiv.org/abs/math/0703066v2

J. Algebra 321 (2009), 1600-1631

Mathematics

Algebraic Geometry

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

Scientific paper

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 $\emph{quasi-bundle}$. 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 $K_S^2=4,6$.

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