Successive minima of line bundles

Florin Ambro; Atsushi Ito

doi:10.1016/j.aim.2020.107045

Successive minima of line bundles

Florin Ambro, Atsushi Ito

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

1 Citation (Scopus)

Abstract

We introduce and study the successive minima of line bundles on proper algebraic varieties. The first (resp. last) minima are the width (resp. Seshadri constant) of the line bundle at very general points. The volume of the line bundle is equivalent to the product of the successive minima. For line bundles on toric varieties, the successive minima are equivalent to the (reciprocal of) usual successive minima of the difference of the moment polytope.

Original language	English
Article number	107045
Journal	Advances in Mathematics
Volume	365
DOIs	https://doi.org/10.1016/j.aim.2020.107045
Publication status	Published - May 13 2020
Externally published	Yes

Keywords

Linear systems
Seshadri constants
Successive minima

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.1016/j.aim.2020.107045

Cite this

@article{9f55790c108c434e9c3a846368c1825c,

title = "Successive minima of line bundles",

abstract = "We introduce and study the successive minima of line bundles on proper algebraic varieties. The first (resp. last) minima are the width (resp. Seshadri constant) of the line bundle at very general points. The volume of the line bundle is equivalent to the product of the successive minima. For line bundles on toric varieties, the successive minima are equivalent to the (reciprocal of) usual successive minima of the difference of the moment polytope.",

keywords = "Linear systems, Seshadri constants, Successive minima",

author = "Florin Ambro and Atsushi Ito",

note = "Funding Information: The first author is grateful to Max Planck Institut f{\"u}r Mathematik in Bonn for its hospitality and financial support. The second author was supported by Grant-in-Aid for Scientific Research 17K14162 . We would like to thank the referee for useful comments and suggestions. Publisher Copyright: {\textcopyright} 2020 Elsevier Inc.",

year = "2020",

month = may,

day = "13",

doi = "10.1016/j.aim.2020.107045",

language = "English",

volume = "365",

journal = "Advances in Mathematics",

issn = "0001-8708",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - Successive minima of line bundles

AU - Ambro, Florin

AU - Ito, Atsushi

N1 - Funding Information: The first author is grateful to Max Planck Institut für Mathematik in Bonn for its hospitality and financial support. The second author was supported by Grant-in-Aid for Scientific Research 17K14162 . We would like to thank the referee for useful comments and suggestions. Publisher Copyright: © 2020 Elsevier Inc.

PY - 2020/5/13

Y1 - 2020/5/13

N2 - We introduce and study the successive minima of line bundles on proper algebraic varieties. The first (resp. last) minima are the width (resp. Seshadri constant) of the line bundle at very general points. The volume of the line bundle is equivalent to the product of the successive minima. For line bundles on toric varieties, the successive minima are equivalent to the (reciprocal of) usual successive minima of the difference of the moment polytope.

AB - We introduce and study the successive minima of line bundles on proper algebraic varieties. The first (resp. last) minima are the width (resp. Seshadri constant) of the line bundle at very general points. The volume of the line bundle is equivalent to the product of the successive minima. For line bundles on toric varieties, the successive minima are equivalent to the (reciprocal of) usual successive minima of the difference of the moment polytope.

KW - Linear systems

KW - Seshadri constants

KW - Successive minima

UR - http://www.scopus.com/inward/record.url?scp=85079415101&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85079415101&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2020.107045

DO - 10.1016/j.aim.2020.107045

M3 - Article

AN - SCOPUS:85079415101

VL - 365

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

M1 - 107045

ER -

Successive minima of line bundles

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this