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# Surfaces with $p_g=q=2$, $K^2=6$, and Albanese Map of Degree $2$

Published:2012-04-12
Printed: Feb 2013
• Matteo Penegini,
Lehrstuhl Mathematik VIII, Universität Bayreuth, NWII, D-95440 Bayreuth, Germany
• Francesco Polizzi,
Dipartimento di Matematica, Università della Calabria, Cubo 30B, 87036, Arcavacata di Rende (Cosenza), Italy
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## Abstract

We classify minimal surfaces of general type with $p_g=q=2$ and $K^2=6$ whose Albanese map is a generically finite double cover. We show that the corresponding moduli space is the disjoint union of three generically smooth irreducible components $\mathcal{M}_{Ia}$, $\mathcal{M}_{Ib}$, $\mathcal{M}_{II}$ of dimension $4$, $4$, $3$, respectively.
 Keywords: surface of general type, abelian surface, Albanese map
 MSC Classifications: 14J29 - Surfaces of general type 14J10 - Families, moduli, classification: algebraic theory