EXAMPLES ON LOEWY FILTRATIONS AND K-STABILITY OF FANO VARIETIES WITH NON-REDUCTIVE AUTOMORPHISM GROUPS

Atsushi Ito

doi:10.5802/aif.3395

EXAMPLES ON LOEWY FILTRATIONS AND K-STABILITY OF FANO VARIETIES WITH NON-REDUCTIVE AUTOMORPHISM GROUPS

Research output: Contribution to journal › Article › peer-review

Abstract

It is known that the automorphism group of a K-polystable Fano manifold is reductive. Codogni and Dervan constructed a canonical filtration of the section ring, called Loewy filtration, and conjectured that the filtration destabilizes any Fano variety with non-reductive automorphism group. In this note, we give a counterexample to their conjecture.

Original language	English
Pages (from-to)	515-537
Number of pages	23
Journal	Annales de l'Institut Fourier
Volume	71
Issue number	2
DOIs	https://doi.org/10.5802/aif.3395
Publication status	Published - 2021
Externally published	Yes

Keywords

K-stability
Loewy filtration

ASJC Scopus subject areas

Algebra and Number Theory
Geometry and Topology

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10.5802/aif.3395

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title = "EXAMPLES ON LOEWY FILTRATIONS AND K-STABILITY OF FANO VARIETIES WITH NON-REDUCTIVE AUTOMORPHISM GROUPS",

abstract = "It is known that the automorphism group of a K-polystable Fano manifold is reductive. Codogni and Dervan constructed a canonical filtration of the section ring, called Loewy filtration, and conjectured that the filtration destabilizes any Fano variety with non-reductive automorphism group. In this note, we give a counterexample to their conjecture.",

keywords = "K-stability, Loewy filtration",

author = "Atsushi Ito",

note = "Funding Information: Keywords: Loewy filtration, K-stability. 2020 Mathematics Subject Classification: 14J45, 14L30, 32Q26. (*) The author was supported by Grant-in-Aid for Scientific Research 17K14162. Publisher Copyright: {\textcopyright} Association des Annales de l{\textquoteright}institut Fourier, 2021.",

year = "2021",

doi = "10.5802/aif.3395",

language = "English",

volume = "71",

pages = "515--537",

journal = "Annales de l'Institut Fourier",

issn = "0373-0956",

publisher = "Association des Annales de l'Institut Fourier",

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T1 - EXAMPLES ON LOEWY FILTRATIONS AND K-STABILITY OF FANO VARIETIES WITH NON-REDUCTIVE AUTOMORPHISM GROUPS

AU - Ito, Atsushi

N1 - Funding Information: Keywords: Loewy filtration, K-stability. 2020 Mathematics Subject Classification: 14J45, 14L30, 32Q26. (*) The author was supported by Grant-in-Aid for Scientific Research 17K14162. Publisher Copyright: © Association des Annales de l’institut Fourier, 2021.

PY - 2021

Y1 - 2021

N2 - It is known that the automorphism group of a K-polystable Fano manifold is reductive. Codogni and Dervan constructed a canonical filtration of the section ring, called Loewy filtration, and conjectured that the filtration destabilizes any Fano variety with non-reductive automorphism group. In this note, we give a counterexample to their conjecture.

AB - It is known that the automorphism group of a K-polystable Fano manifold is reductive. Codogni and Dervan constructed a canonical filtration of the section ring, called Loewy filtration, and conjectured that the filtration destabilizes any Fano variety with non-reductive automorphism group. In this note, we give a counterexample to their conjecture.

KW - K-stability

KW - Loewy filtration

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JF - Annales de l'Institut Fourier

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ER -

EXAMPLES ON LOEWY FILTRATIONS AND K-STABILITY OF FANO VARIETIES WITH NON-REDUCTIVE AUTOMORPHISM GROUPS

Abstract

Keywords

ASJC Scopus subject areas

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