On the projective normality of double coverings over a rational surface

JOURNAL OF ALGEBRA

卷:469

Article

Rajaguru, Biswajit¹  Song, Lei¹ 

[1] Univ Kansas, Dept Math, Lawrence, KS 66045 USA

关键词: Projective normality;    Double covering;    Adjoint divisor;   

DOI  :  10.1016/j.jalgebra.2016.08.024

来源: Elsevier

【 摘 要 】

We study the projective normality of a minimal surface X which is a ramified double covering over a rational surface S with dim vertical bar - Ks vertical bar >= 1. In particular Horikawa surfaces, the minimal surfaces of general type with K-X(2)= 2p(g)(X) - 4, are of this type, up to resolution of singularities. Let pi be the covering map from X to S. We show that the Z(2)-invariant adjoint divisors K-X + r pi(*)A are normally generated, where the integer r >= 3 and A is an ample divisor on S. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free