Tian’s αm,kK^ -invariants on group compactifications

Yan Li; Xiaohua Zhu

doi:10.1007/s00209-020-02591-9

Tian’s αm,kK^ -invariants on group compactifications

Yan Li^*, Xiaohua Zhu

^*Corresponding author for this work

School of Mathematics and Statistics

Peking University

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

2 Citations (Scopus)

Abstract

In this paper, we compute Tian’s αm,kK×K-invariant on a polarized G-group compactification, where K denotes a maximal compact subgroup of a connected complex reductive group G. We prove that Tian’s conjecture (see Conjecture 1.1 below) is true for αm,kK×K-invariant on such manifolds when k= 1 , but it fails in general by producing counter-examples when k≥ 2.

Original language	English
Pages (from-to)	231-259
Number of pages	29
Journal	Mathematische Zeitschrift
Volume	298
Issue number	1-2
DOIs	https://doi.org/10.1007/s00209-020-02591-9
Publication status	Published - Jun 2021

Keywords

Group compactifications
Polytopes
Toric manifolds
α(M) -invariant

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Li, Y., & Zhu, X. (2021). Tian’s αm,kK^ -invariants on group compactifications. Mathematische Zeitschrift, 298(1-2), 231-259. https://doi.org/10.1007/s00209-020-02591-9

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abstract = "In this paper, we compute Tian{\textquoteright}s αm,kK×K-invariant on a polarized G-group compactification, where K denotes a maximal compact subgroup of a connected complex reductive group G. We prove that Tian{\textquoteright}s conjecture (see Conjecture 1.1 below) is true for αm,kK×K-invariant on such manifolds when k= 1 , but it fails in general by producing counter-examples when k≥ 2.",

keywords = "Group compactifications, Polytopes, Toric manifolds, α(M) -invariant",

author = "Yan Li and Xiaohua Zhu",

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AU - Li, Yan

AU - Zhu, Xiaohua

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AB - In this paper, we compute Tian’s αm,kK×K-invariant on a polarized G-group compactification, where K denotes a maximal compact subgroup of a connected complex reductive group G. We prove that Tian’s conjecture (see Conjecture 1.1 below) is true for αm,kK×K-invariant on such manifolds when k= 1 , but it fails in general by producing counter-examples when k≥ 2.

KW - Group compactifications

KW - Polytopes

KW - Toric manifolds

KW - α(M) -invariant

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ER -

Tian’s αm,kK^ -invariants on group compactifications

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Keywords

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