Characterization of projective spaces by Seshadri constants

Yuchen Liu; Ziquan Zhuang

doi:10.1007/s00209-017-1941-9

Characterization of projective spaces by Seshadri constants

Yuchen Liu, Ziquan Zhuang^*

^*Corresponding author for this work

Mathematics

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

17 Scopus citations

Abstract

We prove that an n-dimensional complex projective variety is isomorphic to Pⁿ if the Seshadri constant of the anti-canonical divisor at some smooth point is greater than n. We also classify complex projective varieties with Seshadri constants equal to n.

Original language	English (US)
Pages (from-to)	25-38
Number of pages	14
Journal	Mathematische Zeitschrift
Volume	289
Issue number	1-2
DOIs	https://doi.org/10.1007/s00209-017-1941-9
State	Published - Jun 1 2018

Funding

Acknowledgements We would like to thank our advisor János Kollár for his constant support, encouragement and numerous inspiring conversations. We would like to thank Thomas Bauer, Pedro Montero, Tomasz Szemberg and Chenyang Xu for helpful comments. The first author also wishes to thank Xiaowei Wang for useful discussions, and Kento Fujita for his interest and encouragement. The first author is partially supported by NSF grants DMS-0968337 and DMS-1362960.

Keywords

Classification
Fano varieties
Projective space
Seshadri constants

ASJC Scopus subject areas

General Mathematics

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10.1007/s00209-017-1941-9

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title = "Characterization of projective spaces by Seshadri constants",

abstract = "We prove that an n-dimensional complex projective variety is isomorphic to Pn if the Seshadri constant of the anti-canonical divisor at some smooth point is greater than n. We also classify complex projective varieties with Seshadri constants equal to n.",

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AB - We prove that an n-dimensional complex projective variety is isomorphic to Pn if the Seshadri constant of the anti-canonical divisor at some smooth point is greater than n. We also classify complex projective varieties with Seshadri constants equal to n.

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KW - Projective space

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Characterization of projective spaces by Seshadri constants

Abstract

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Keywords

ASJC Scopus subject areas

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