A connected component of the moduli space of surfaces of general type with p_g=0

1999/10/04 by Margarida Mendes Lopes, M. Mendes Lopes, Rita Pardini +3 · 4 citations
Mathematics · #14J10 #14J29 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #math.AG #msc:14J10 #msc:14J29

paper · pdf · doi:10.48550/arxiv.math/9910012

LaTeX 2.09, 20 pages

arxiv created 1999/10/04 · openalex publication_date 1999/10/04 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let S be a minimal surface of general type with p_g(S)=0 and such that the bicanonical map ϕ:S→ \pp^K2_S is a morphism: then the degree of ϕ is at most 4 and if it is equal to 4 then K²_S≤ 6. Here we prove that if K²_S=6 and °ϕ=4 then S is a so-called \em Burniat surface. In addition we show that minimal surfaces with p_g=0, K²=6 and bicanonical map of degree 4 form a 4-dimensional irreducible connected component of the moduli space of surfaces of general type.

Cited by

• A survey on the bicanonical map of surfaces with p_g=0 and K²≥ 2
• Surfaces with p_g = 0, K² = 5 and bicanonical maps of degree 4
• A note on a theorem of Xiao Gang
• A new family of surfaces with p_g=0 and K²=3

Related

• A characterization of Burniat surfaces with K²=4 and of non nodal type
• Surfaces with p_g = 0, K² = 5 and bicanonical maps of degree 4
• The classification of surfaces with p_g=0, K²=6 and non birational bicanonical map
• The bicanonical map of surfaces with p_g=0 and K² ≥ 7
• The degree of the bicanonical map of a surface with p_g=0