A characterization of Burniat surfaces with K²=4 and of non nodal type

2014/07/22 by YongJoo Shin, Shin, YongJoo
Mathematics · #Algebraic Geometry and Number Theory #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.AG #msc:14J10 #msc:14J29

paper · pdf · doi:10.48550/arxiv.1407.5785

The proof of Step 1 in Proof of Theorem 1.1 was changed. It has been accepted for publication in SCIENCE CHINA Mathematics

arxiv created 2015/07/13 · arxiv updated 2015/07/15

Abstract

Let S be a minimal surface of general type with p_g(S)=0 and K²_S=4. Assume the bicanonical map φ of S is a morphism of degree 4 such that the image of φ is smooth. Then we prove that the surface S is a Burniat surface with K²=4 and of non nodal type.

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