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

3 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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10.1007/s00209-020-02591-9

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title = "Tian{\textquoteright}s αm,kK\textasciicircum{} -invariants on group compactifications",

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",

note = "Publisher Copyright: {\textcopyright} 2020, Springer-Verlag GmbH Germany, part of Springer Nature.",

year = "2021",

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doi = "10.1007/s00209-020-02591-9",

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TY - JOUR

T1 - Tian’s αm,kK^ -invariants on group compactifications

AU - Li, Yan

AU - Zhu, Xiaohua

PY - 2021/6

Y1 - 2021/6

N2 - 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.

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

UR - https://www.scopus.com/pages/publications/85089535535

U2 - 10.1007/s00209-020-02591-9

DO - 10.1007/s00209-020-02591-9

M3 - Article

AN - SCOPUS:85089535535

SN - 0025-5874

VL - 298

SP - 231

EP - 259

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

IS - 1-2

ER -

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

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Keywords

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