K-Unstable Singular del Pezzo Surfaces Without Anticanonical Polar Cylinder-Reference-Cited by-同舟云学术

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K-Unstable Singular del Pezzo Surfaces Without Anticanonical Polar Cylinder

Published:2024-08-14 Issue: Volume: Page:
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Kim In-Kyun¹,Kim Jaehyun²,Won Joonyeong²

Affiliation:

1. June E Huh Center for Mathematical Challenges , Korea Institute for Advanced Study, 85 Hoegiro Dongdaemun-gu, Seoul 02455, Republic of Korea

2. Department of Mathematics , Ewha Womans University 52, Ewhayeodae-gil, Seodaemun-gu, Seoul, 03760, Republic of Korea

Abstract

Abstract We prove the existence of singular del Pezzo surfaces that are neither K-semistable nor contain any anticanonical polar cylinder.

Funder

National Research Foundation of Korea

Publisher

Oxford University Press (OUP)

Link

https://academic.oup.com/imrn/advance-article-pdf/doi/10.1093/imrn/rnae175/58812863/rnae175.pdf

Reference29 articles.

1. Reductivity of the automorphism group of $K$-polystable Fano varieties;Alper;Invent. Math.,2020

2. Kähler–Einstein metrics for some quasi-smooth log del Pezzo surfaces;Araujo;Trans. Amer. Math. Soc.,2002

3. Thresholds, valuations, and K-stability;Blum;Adv. Math.,2020

4. On the geometry of Sasakian–Einstein 5-manifolds;Boyer;Math. Ann.,2003

5. Birational geometry, Kähler–Einstein metrics and degenerations;Cheltsov,2023

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