Sakai's theorem for Q-divisors on surfaces and applications

Ye, F.; Zhang, T.; Zhu, Z.

Abstract

In this paper, we present a characterization of a big Q-divisor D on a smooth projective surface S with D2 > 0 and H1(OS(−D)) = 0, which generalizes a result of Sakai [Sak90] for D integral. As applications of this result for Q-divisors, we prove results on base-pointfreeness and very-ampleness of the adjoint linear system |KS + D|. These results can be viewed as refinements of previous results on smooth surfaces of Ein-Lazarsfeld [EL93] and Ma¸sek [Ma¸s99].

Citation

Ye, F., Zhang, T., & Zhu, Z. (2018). Sakai's theorem for Q-divisors on surfaces and applications. Asian Journal of Mathematics, 22(4), 761-786. https://doi.org/10.4310/ajm.2018.v22.n4.a8

• Journal Article Type: Article
• Acceptance Date: Jun 14, 2017
• Online Publication Date: Aug 31, 2018
• Publication Date: Aug 31, 2018
• Deposit Date: Jun 15, 2017
• Publicly Available Date: Apr 30, 2019
• Journal: Asian Journal of Mathematics
• Print ISSN: 1093-6106
• Electronic ISSN: 1945-0036
• Publisher: International Press
• Peer Reviewed: Peer Reviewed
• Volume: 22
• Issue: 4
• Pages: 761-786
• DOI: https://doi.org/10.4310/ajm.2018.v22.n4.a8
• Public URL: https://durham-repository.worktribe.com/output/1376948