A note on a theorem of Xiao Gang

الأصل · EN

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 | 2Kₛ| is base point free, whenever pg≥ 1, the part of this theorem concerning surfaces with pg≥ 1 became trivial. In this note a new proof of this theorem for surfaces with pg=0 is presented.