Toric Fano manifolds that do not admit extremal Kähler metrics

Fuente: arXiv
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Main Authors: Hwang, DongSeon, Sato, Hiroshi, Yotsutani, Naoto
Format: Preprint
Published: 2024
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_version_ 1866929617983504384
author Hwang, DongSeon
Sato, Hiroshi
Yotsutani, Naoto
author_facet Hwang, DongSeon
Sato, Hiroshi
Yotsutani, Naoto
contents We show that there exists a toric Fano manifold of dimension $10$ that does not admit an extremal Kähler metric in the first Chern class, answering a question of Mabuchi. By taking a product with a suitable toric Fano manifold, one can also produce a toric Fano manifold of dimension $n$ admitting no extremal Kähler metric in the first Chern class for each $n \geq 11$.
format Preprint
id arxiv_https___arxiv_org_abs_2411_17574
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Toric Fano manifolds that do not admit extremal Kähler metrics
Hwang, DongSeon
Sato, Hiroshi
Yotsutani, Naoto
Algebraic Geometry
Differential Geometry
53C55, 14L24, 14M25
We show that there exists a toric Fano manifold of dimension $10$ that does not admit an extremal Kähler metric in the first Chern class, answering a question of Mabuchi. By taking a product with a suitable toric Fano manifold, one can also produce a toric Fano manifold of dimension $n$ admitting no extremal Kähler metric in the first Chern class for each $n \geq 11$.
title Toric Fano manifolds that do not admit extremal Kähler metrics
topic Algebraic Geometry
Differential Geometry
53C55, 14L24, 14M25
url https://arxiv.org/abs/2411.17574