Alpha invariants of birationally bi-rigid Fano 3-folds I

In Kyun Kim; Takuzo Okada; Joonyeong Won

doi:10.1007/s40879-020-00441-w

Alpha invariants of birationally bi-rigid Fano 3-folds I

In Kyun Kim
, Takuzo Okada
, Joonyeong Won

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

3 Scopus citations

Abstract

We compute global log canonical thresholds of certain birationally bi-rigid Fano 3-folds embedded in weighted projective spaces as complete intersections of codimension 2 and prove that they admit an orbifold Kähler–Einstein metric and are K-stable. As an application, we give examples of super-rigid affine Fano 4-folds.

Original language	English
Pages (from-to)	272-308
Number of pages	37
Journal	European Journal of Mathematics
Volume	7
Issue number	1
DOIs	https://doi.org/10.1007/s40879-020-00441-w
State	Published - Mar 2021
Externally published	Yes

Bibliographical note

Funding Information:
The first author was supported by the National Research Foundation of Korea (NRF-2020R1A2C4002510). The second author is partially supported by JSPS KAKENHI Grant Number JP18K03216. The third author was supported by the National Research Foundation of Korea (NRF-2020R1A2C1A01008018) and a KIAS Individual Grant (SP037003) via the Center for Mathematical Challenges at Korea Institute for Advanced Study.

Publisher Copyright:
© 2020, Springer Nature Switzerland AG.

Keywords

Delta invariant
K-stability
Log del Pezzo surface

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10.1007/s40879-020-00441-w

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abstract = "We compute global log canonical thresholds of certain birationally bi-rigid Fano 3-folds embedded in weighted projective spaces as complete intersections of codimension 2 and prove that they admit an orbifold K{\"a}hler–Einstein metric and are K-stable. As an application, we give examples of super-rigid affine Fano 4-folds.",

keywords = "Delta invariant, K-stability, Log del Pezzo surface",

author = "Kim, \{In Kyun\} and Takuzo Okada and Joonyeong Won",

note = "Funding Information: The first author was supported by the National Research Foundation of Korea (NRF-2020R1A2C4002510). The second author is partially supported by JSPS KAKENHI Grant Number JP18K03216. The third author was supported by the National Research Foundation of Korea (NRF-2020R1A2C1A01008018) and a KIAS Individual Grant (SP037003) via the Center for Mathematical Challenges at Korea Institute for Advanced Study. Publisher Copyright: {\textcopyright} 2020, Springer Nature Switzerland AG.",

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doi = "10.1007/s40879-020-00441-w",

language = "English",

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T1 - Alpha invariants of birationally bi-rigid Fano 3-folds I

AU - Kim, In Kyun

AU - Okada, Takuzo

AU - Won, Joonyeong

N1 - Funding Information: The first author was supported by the National Research Foundation of Korea (NRF-2020R1A2C4002510). The second author is partially supported by JSPS KAKENHI Grant Number JP18K03216. The third author was supported by the National Research Foundation of Korea (NRF-2020R1A2C1A01008018) and a KIAS Individual Grant (SP037003) via the Center for Mathematical Challenges at Korea Institute for Advanced Study. Publisher Copyright: © 2020, Springer Nature Switzerland AG.

PY - 2021/3

Y1 - 2021/3

N2 - We compute global log canonical thresholds of certain birationally bi-rigid Fano 3-folds embedded in weighted projective spaces as complete intersections of codimension 2 and prove that they admit an orbifold Kähler–Einstein metric and are K-stable. As an application, we give examples of super-rigid affine Fano 4-folds.

AB - We compute global log canonical thresholds of certain birationally bi-rigid Fano 3-folds embedded in weighted projective spaces as complete intersections of codimension 2 and prove that they admit an orbifold Kähler–Einstein metric and are K-stable. As an application, we give examples of super-rigid affine Fano 4-folds.

KW - Delta invariant

KW - K-stability

KW - Log del Pezzo surface

UR - https://www.scopus.com/pages/publications/85096972645

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DO - 10.1007/s40879-020-00441-w

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AN - SCOPUS:85096972645

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VL - 7

SP - 272

EP - 308

JO - European Journal of Mathematics

JF - European Journal of Mathematics

IS - 1

ER -

Alpha invariants of birationally bi-rigid Fano 3-folds I

Abstract

Bibliographical note

Keywords

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