A note on a theorem of Xiao Gang

2003/02/26 by Margarida Mendes Lopes, Lopes, Margarida Mendes
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Meromorphic and Entire Functions #math.AG

paper · pdf · doi:10.48550/arxiv.math/0302321

Latex, 4 pages

arxiv created 2003/02/26 · openalex publication_date 2003/02/26 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In 1985 Xiao Gang proved that the bicanonical system of a complex surface S of general type with p₂(S)>2 is not composed of a pencil [Bull. Soc. Math. France, 113 (1985), 23--51]. When in the end of the 80's it was finally proven that | 2K_S| is base point free, whenever p_g≥ 1, the part of this theorem concerning surfaces with p_g≥ 1 became trivial. In this note a new proof of this theorem for surfaces with p_g=0 is presented.

Citations

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

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