We construct a new family of minimal surfaces of general type with pg = q = 2 and K2 = 6, whose Albanese map is a quadruple cover of an abelian surface with polarization of type (1, 3). We also show that this family provides an irreducible component of the moduli space of surfaces with pg = q = 2 and K2 = 6. Finally, we prove that such a component is generically smooth of dimension 4 and that it contains the two-dimensional family of product–quotient examples previously constructed by the first author. The main tools we use are the Fourier–Mukai transform and the Schr¨odinger representation of the finite Heisenberg group H3.

A new family of surfaces with pg=q=2 and K2=6 whose Albanese map has degree 4 / M. Penegini, F. Polizzi. - In: JOURNAL OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6107. - 90:3(2014), pp. 741-762.

A new family of surfaces with pg=q=2 and K2=6 whose Albanese map has degree 4

M. Penegini
;
2014

Abstract

We construct a new family of minimal surfaces of general type with pg = q = 2 and K2 = 6, whose Albanese map is a quadruple cover of an abelian surface with polarization of type (1, 3). We also show that this family provides an irreducible component of the moduli space of surfaces with pg = q = 2 and K2 = 6. Finally, we prove that such a component is generically smooth of dimension 4 and that it contains the two-dimensional family of product–quotient examples previously constructed by the first author. The main tools we use are the Fourier–Mukai transform and the Schr¨odinger representation of the finite Heisenberg group H3.
Settore MAT/03 - Geometria
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/250863
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