Extremal metrics on the total space of destabilising test configurations

Lars Martin Sektnan; Cristiano Spotti

doi:10.1007/s00208-023-02601-1

Extremal metrics on the total space of destabilising test configurations

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

Abstract

We construct extremal metrics on the total space of certain destabilising test configurations for strictly semistable Kähler manifolds. This produces infinitely many new examples of manifolds admitting extremal Kähler metrics. It also shows for such metrics a new phenomenon of jumping of the complex structure along fibres.

Original language	English
Journal	Mathematische Annalen
Volume	388
Issue	4
Pages (from-to)	3427-3461
Number of pages	35
ISSN	0025-5831
DOIs	https://doi.org/10.1007/s00208-023-02601-1
Publication status	Published - Apr 2024

Keywords

32Q15
32Q20
32Q26
53C55

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10.1007/s00208-023-02601-1Licence: CC BY

Cite this

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title = "Extremal metrics on the total space of destabilising test configurations",

abstract = "We construct extremal metrics on the total space of certain destabilising test configurations for strictly semistable K{\"a}hler manifolds. This produces infinitely many new examples of manifolds admitting extremal K{\"a}hler metrics. It also shows for such metrics a new phenomenon of jumping of the complex structure along fibres.",

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author = "Sektnan, {Lars Martin} and Cristiano Spotti",

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AB - We construct extremal metrics on the total space of certain destabilising test configurations for strictly semistable Kähler manifolds. This produces infinitely many new examples of manifolds admitting extremal Kähler metrics. It also shows for such metrics a new phenomenon of jumping of the complex structure along fibres.

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M3 - Journal article

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EP - 3461

JO - Mathematische Annalen

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Extremal metrics on the total space of destabilising test configurations

Abstract

Keywords

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