Toric Sasaki–Einstein metrics with conical singularities

We show that any toric Kähler cone with smooth compact cross-section admits a family of Calabi–Yau cone metrics with conical singularities along its toric divisors. The family is parametrized by the Reeb cone and the angles are given explicitly in terms of the Reeb vector field. The result is optima...

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Main Authors: Martin de Borbon, Eveline Legendre
Format: Default Article
Published: 2022
Subjects:
Applied mathematics
Mathematical physics
Pure mathematics
General Mathematics
Online Access:https://hdl.handle.net/2134/24526288.v1
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author Martin de Borbon
Eveline Legendre
author_facet Martin de Borbon
Eveline Legendre
author_sort Martin de Borbon (16976562)
collection Figshare
description We show that any toric Kähler cone with smooth compact cross-section admits a family of Calabi–Yau cone metrics with conical singularities along its toric divisors. The family is parametrized by the Reeb cone and the angles are given explicitly in terms of the Reeb vector field. The result is optimal, in the sense that any toric Calabi–Yau cone metric with conical singularities along the toric divisor (and smooth elsewhere) belongs to this family. We also provide examples and interpret our results in terms of Sasaki–Einstein metrics.
format Default
Article
id rr-article-24526288
institution Loughborough University
publishDate 2022
record_format Figshare
spelling rr-article-245262882022-05-04T00:00:00Z Toric Sasaki–Einstein metrics with conical singularities Martin de Borbon (16976562) Eveline Legendre (17361331) Applied mathematics Mathematical physics Pure mathematics General Mathematics <p>We show that any toric Kähler cone with smooth compact cross-section admits a family of Calabi–Yau cone metrics with conical singularities along its toric divisors. The family is parametrized by the Reeb cone and the angles are given explicitly in terms of the Reeb vector field. The result is optimal, in the sense that any toric Calabi–Yau cone metric with conical singularities along the toric divisor (and smooth elsewhere) belongs to this family. We also provide examples and interpret our results in terms of Sasaki–Einstein metrics.</p> 2022-05-04T00:00:00Z Text Journal contribution 2134/24526288.v1 https://figshare.com/articles/journal_contribution/Toric_Sasaki_Einstein_metrics_with_conical_singularities/24526288 CC BY 4.0
spellingShingle Applied mathematics
Mathematical physics
Pure mathematics
General Mathematics
Martin de Borbon
Eveline Legendre
Toric Sasaki–Einstein metrics with conical singularities
title Toric Sasaki–Einstein metrics with conical singularities
title_full Toric Sasaki–Einstein metrics with conical singularities
title_fullStr Toric Sasaki–Einstein metrics with conical singularities
title_full_unstemmed Toric Sasaki–Einstein metrics with conical singularities
title_short Toric Sasaki–Einstein metrics with conical singularities
title_sort toric sasaki–einstein metrics with conical singularities
topic Applied mathematics
Mathematical physics
Pure mathematics
General Mathematics
url https://hdl.handle.net/2134/24526288.v1

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