Okounkov bodies and zariski decompositions on surfaces

Sung Rak Choi; Jinhyung Park; Joonyeong Won

doi:10.4134/BKMS.b160686

Okounkov bodies and zariski decompositions on surfaces

Sung Rak Choi, Jinhyung Park, Joonyeong Won

Department of Mathematics

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

3 Scopus citations

Abstract

The purpose of this paper is to investigate the close relation between Okounkov bodies and Zariski decompositions of pseudoeffective divisors on smooth projective surfaces. Firstly, we completely determine the limiting Okounkov bodies on such surfaces, and give applications to Nakayama constants and Seshadri constants. Secondly, we study how the shapes of Okounkov bodies change as we vary the divisors in the big cone.

Original language	English
Pages (from-to)	1677-1697
Number of pages	21
Journal	Bulletin of the Korean Mathematical Society
Volume	54
Issue number	5
DOIs	https://doi.org/10.4134/BKMS.b160686
State	Published - 2017

Bibliographical note

Publisher Copyright:
© 2017 Korean Mathematial Soiety.

Keywords

Asymptotic invariants of a divisor
Okounkov body
Pseudoeffective divisor
Zariski decomposition

Access to Document

10.4134/BKMS.b160686

Cite this

@article{4b6a8669365744f582ea4a4ec1dfddce,

title = "Okounkov bodies and zariski decompositions on surfaces",

abstract = "The purpose of this paper is to investigate the close relation between Okounkov bodies and Zariski decompositions of pseudoeffective divisors on smooth projective surfaces. Firstly, we completely determine the limiting Okounkov bodies on such surfaces, and give applications to Nakayama constants and Seshadri constants. Secondly, we study how the shapes of Okounkov bodies change as we vary the divisors in the big cone.",

keywords = "Asymptotic invariants of a divisor, Okounkov body, Pseudoeffective divisor, Zariski decomposition",

author = "Choi, {Sung Rak} and Jinhyung Park and Joonyeong Won",

note = "Publisher Copyright: {\textcopyright} 2017 Korean Mathematial Soiety.",

year = "2017",

doi = "10.4134/BKMS.b160686",

language = "English",

volume = "54",

pages = "1677--1697",

journal = "Bulletin of the Korean Mathematical Society",

issn = "1015-8634",

publisher = "Korean Mathematical Society",

number = "5",

}

TY - JOUR

T1 - Okounkov bodies and zariski decompositions on surfaces

AU - Choi, Sung Rak

AU - Park, Jinhyung

AU - Won, Joonyeong

PY - 2017

Y1 - 2017

N2 - The purpose of this paper is to investigate the close relation between Okounkov bodies and Zariski decompositions of pseudoeffective divisors on smooth projective surfaces. Firstly, we completely determine the limiting Okounkov bodies on such surfaces, and give applications to Nakayama constants and Seshadri constants. Secondly, we study how the shapes of Okounkov bodies change as we vary the divisors in the big cone.

AB - The purpose of this paper is to investigate the close relation between Okounkov bodies and Zariski decompositions of pseudoeffective divisors on smooth projective surfaces. Firstly, we completely determine the limiting Okounkov bodies on such surfaces, and give applications to Nakayama constants and Seshadri constants. Secondly, we study how the shapes of Okounkov bodies change as we vary the divisors in the big cone.

KW - Asymptotic invariants of a divisor

KW - Okounkov body

KW - Pseudoeffective divisor

KW - Zariski decomposition

UR - http://www.scopus.com/inward/record.url?scp=85030331055&partnerID=8YFLogxK

U2 - 10.4134/BKMS.b160686

DO - 10.4134/BKMS.b160686

M3 - Article

AN - SCOPUS:85030331055

SN - 1015-8634

VL - 54

SP - 1677

EP - 1697

JO - Bulletin of the Korean Mathematical Society

JF - Bulletin of the Korean Mathematical Society

IS - 5

ER -

Okounkov bodies and zariski decompositions on surfaces

Abstract

Bibliographical note

Keywords

Access to Document

Fingerprint

Cite this