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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 surface of general type, abelian surface, Albanese map
MSC Classifications: 14J29, 14J10 show english descriptions Surfaces of general type
Families, moduli, classification: algebraic theory
14J29 - Surfaces of general type
14J10 - Families, moduli, classification: algebraic theory
 

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