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

Fei Ye; Tong Zhang; Zhixian Zhu

doi:10.4310/AJM.2018.v22.n4.a8

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

Fei Ye
, Tong Zhang
, Zhixian Zhu

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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(O_S(⌈-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 |K_S ⌈+D⌉|. These results can be viewed as refinements of previous results on smooth surfaces of Ein-Lazarsfeld [EL93] and Maşek [Maş99].

Original language	English
Pages (from-to)	761-786
Number of pages	26
Journal	Asian Journal of Mathematics
Volume	22
Issue number	4
DOIs	https://doi.org/10.4310/AJM.2018.v22.n4.a8
State	Published - 2018

Keywords

Adjoint linear system
Vanishing theorem
ℚ-divisor

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10.4310/AJM.2018.v22.n4.a8

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title = "Sakai'S theorem for ℚ-divisors on surfaces and applications",

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{\c s}ek [Ma{\c s}99].",

keywords = "Adjoint linear system, Vanishing theorem, ℚ-divisor",

author = "Fei Ye and Tong Zhang and Zhixian Zhu",

note = "Publisher Copyright: {\textcopyright} 2018 International Press.",

year = "2018",

doi = "10.4310/AJM.2018.v22.n4.a8",

language = "英语",

volume = "22",

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T1 - Sakai'S theorem for ℚ-divisors on surfaces and applications

AU - Ye, Fei

AU - Zhang, Tong

AU - Zhu, Zhixian

PY - 2018

Y1 - 2018

N2 - 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 Maşek [Maş99].

AB - 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 Maşek [Maş99].

KW - Adjoint linear system

KW - Vanishing theorem

KW - ℚ-divisor

UR - https://www.scopus.com/pages/publications/85055736297

U2 - 10.4310/AJM.2018.v22.n4.a8

DO - 10.4310/AJM.2018.v22.n4.a8

M3 - 文章

AN - SCOPUS:85055736297

SN - 1093-6106

VL - 22

SP - 761

EP - 786

JO - Asian Journal of Mathematics

JF - Asian Journal of Mathematics

IS - 4

ER -

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

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Keywords

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