# Standard isotrivial fibrations with p g=q=1. II - Mathematics > Algebraic Geometry

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Abstract: A smooth, projective surface $S$ is called a $\emph{standard isotrivialfibration}$ if there exists a finite group $G$ which acts faithfully on twosmooth projective curves $C$ and $F$ so that $S$ is isomorphic to the minimaldesingularization of $T:=C \times F-G$. Standard isotrivial fibrations ofgeneral type with $p g=q=1$ have been classified in \cite{Pol07} under theassumption that $T$ has only Rational Double Points as singularities. In thepresent paper we extend this result, classifying all cases where $S$ is aminimal model. As a by-product, we provide the first examples of minimalsurfaces of general type with $p g=q=1$, $K S^2=5$ and Albanese fibration ofgenus 3. Finally, we show with explicit examples that the case where $S$ is notminimal actually occurs.

Author: ** Ernesto Mistretta, Francesco Polizzi**

Source: https://arxiv.org/