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Keum-Naie-Mendes Lopes-Pardini surfaces yield an irreducible component of the moduli space (2013)

Chen, Y.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2013-09-13

Description: We construct a family of minimal smooth surfaces of general type with K 2 = 3 and p g = 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 K 2 = 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.

Print ISSN: 0024-6093

Electronic ISSN: 1469-2120

Topics: Mathematics

Published by Oxford University Press

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