A note on a theorem of Xiao Gang

Details A note on a theorem of Xiao Gang A note on a theorem of Xiao Gang

2003-02-26

arxiv.org/abs/math/0302321v1

Mathematics

Algebraic Geometry

Latex, 4 pages

Scientific paper

In 1985 Xiao Gang proved that the bicanonical system of a complex surface $S$ of general type with $p_2(S)>2$ 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 $p_g\geq 1$, the part of this theorem concerning surfaces with $p_g\geq 1$ became trivial. In this note a new proof of this theorem for surfaces with $p_g=0$ is presented.

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