Some (big) irreducible components of the moduli space of minimal surfaces of general type with $p_g=q=1$ and $K^2=4$

Abstract

In this paper we study the minimal surfaces of general type with $p_g=q=1$ and $K^2=4$ whose Albanese general fibre has genus 2, classifying those such that the direct image (under the Albanese morphism) of the bicanonical sheaf is sum of line bundles. We find 8 unirational families, all of dimension strictly bigger than the expected one. These families are pairwise disjoint irreducible components of the moduli space of minimal surfaces of general type.

20 pages. v2: improved introduction, final version to appear on Rend. Lincei Mat. Appl

References in corpus (1)

• Quotients of products of curves, new surfaces with $p_g=0$ and their fundamental groups