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Catanese and O . Debarre , ‘ Surfaces with K 2 = 2 , p g = 1 , q = 0 ’
- Publisher
- Wiley
- Copyright
- © London Mathematical Society
- ISSN
- 0024-6093
- eISSN
- 1469-2120
- DOI
- 10.1112/blms/bdt021
- Publisher site
- See Article on Publisher Site
Abstract
We construct a family of minimal smooth surfaces of general type with K2 = 3 and pg = 0, which are finite (ℤ/2ℤ)2‐covers of the 4‐nodal cubic surface. This turns out to be a five‐dimensional subfamily of the six‐dimensional family constructed by Mendes Lopes and Pardini, which realizes the Keum–Naie surfaces with K2 = 3 as degenerations. We show that the base of the Kuranishi family of a general surface in our subfamily is smooth. We prove that the closure of the corresponding subset of the Keum–Naie–Mendes Lopes–Pardini surfaces is an irreducible component of the Gieseker moduli space. As an important byproduct, it is shown that, for the surfaces in this irreducible component, the degree of the bicanonical map can only be 2 or 4.
Journal
Bulletin of the London Mathematical Society – Wiley
Published: Oct 1, 2013