Resumen de Algebraic surfaces of general type with p_g=q=1 and genus 2 Albanese fibrations

Songbo Ling

• In this paper, we study algebraic surfaces of general type with p_g=q=1 and genus 2 Albanese fibrations. We first study the examples of surfaces with p_g=q=1, K^2=5 and genus 2 Albanese fibrations constructed by Catanese using singular bidouble covers of \mathbb {P}^2. We prove that these surfaces give an irreducible and connected component of \mathcal {M}_{1,1}^{5,2}, the Gieseker moduli space of surfaces of general type with p_g=q=1, K^2=5 and genus 2 Albanese fibrations. Then by constructing surfaces with p_g=q=1,K^2=3 and a genus 2 Albanese fibration such that the number of the summands of the direct image of the bicanonical sheaf (under the Albanese map) is 2, we give a negative answer to a question of Pignatelli.