Premium
Keum–Naie–Mendes Lopes–Pardini surfaces yield an irreducible component of the moduli space
Author(s) -
Chen Yifan
Publication year - 2013
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdt021
Subject(s) - mathematics , moduli space , irreducible component , subfamily , pure mathematics , component (thermodynamics) , surface (topology) , space (punctuation) , combinatorics , geometry , mathematical analysis , computer science , differential algebraic equation , ordinary differential equation , physics , differential equation , thermodynamics , biochemistry , chemistry , gene , operating system
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.