Bicanonical and adjoint linear systems on surfaces of general type

Meng Chen and Eckart Viehweg

Vol. 219 (2005), No. 1, 83–95

DOI: 10.2140/pjm.2005.219.83

Abstract

This note contains a new proof of a theorem of Gang Xiao saying that the bicanonical map of a surface S of general type is generically finite if and only if p₂(S) > 2. Such properties are also studied for adjoint linear systems |K_S + L|, where L is any divisor with h⁰(S,𝒪_S(L)) ≥ 2.

Keywords

bicanonical map, algebraic surface, adjoint linear system

Mathematical Subject Classification 2000

Primary: 14J29, 14J25, 14H10

Milestones

Received: 22 September 2003

Published: 1 March 2005