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Surfaces with pg = q = 2, K2 = 6, and Albanese Map of Degree 2

Published online by Cambridge University Press:  20 November 2018

Matteo Penegini  and
Francesco Polizzi
Matteo Penegini
Affiliation:
Lehrstuhl Mathematik VIII, Universität Bayreuth, NWII, D-95440 Bayreuth, Germany, e-mail: matteo.penegini@uni-bayreuth.de
Francesco Polizzi
Affiliation:
Dipartimento di Matematica, Università della Calabria, Cubo 30B, 87036, Arcavacata di Rende (Cosenza), Italy, e-mail: polizzi@mat.unical.it
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Abstract

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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

14J2914J10surface of general typeabelian surfaceAlbanese map
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 65 , Issue 1 , 01 February 2013 , pp. 195 - 221
Copyright
Copyright © Canadian Mathematical Society 2013

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