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Mat. Sb., 2009, Volume 200, Number 1, Pages 97–136 (Mi msb4519)  

This article is cited in 5 scientific papers (total in 5 papers)

Extremal metrics on two Fano varieties

I. A. Cheltsov

University of Edinburgh

Abstract: We prove the existence of an orbifold Kähler-Einstein metric on a general hypersurface in $\mathbb P(1^3,2,2)$ of degree 6 and a general hypersurface in $\mathbb P(1^3,2,3)$ of degree 7.
Bibliography: 50 titles.

Keywords: Fano varieties, Kähler-Einstein metric, log-canonical threshold, Tian alpha-invariant.

DOI: https://doi.org/10.4213/sm4519

Full text: PDF file (735 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2009, 200:1, 95–132

Bibliographic databases:

UDC: 512.7
MSC: Primary 14J45, 32Q20; Secondary 14J17
Received: 07.02.2008 and 04.04.2008

Citation: I. A. Cheltsov, “Extremal metrics on two Fano varieties”, Mat. Sb., 200:1 (2009), 97–136; Sb. Math., 200:1 (2009), 95–132

Citation in format AMSBIB
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  • https://doi.org/10.4213/sm4519
  • http://mi.mathnet.ru/eng/msb/v200/i1/p97

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. I. A. Cheltsov, K. A. Shramov, “Extremal Metrics on del Pezzo Threefolds”, Proc. Steklov Inst. Math., 264 (2009), 30–44  mathnet  crossref  mathscinet  isi  elib  elib
    2. Cheltsov I., Park J., “Birational Rigidity and Main Theorem”, Mem. Am. Math. Soc., 246:1167 (2017), 1+  mathscinet  isi
    3. Kim I.-K., Okada T., Won J., “Alpha Invariants of Birationally Rigid Fano Three-Folds”, Int. Math. Res. Notices, 2018, no. 9, 2745–2800  crossref  mathscinet  isi
    4. Pukhlikov A.V., “Canonical and Log Canonical Thresholds of Fano Complete Intersections”, Eur. J. Math., 4:1, 1, SI (2018), 381–398  crossref  mathscinet  zmath  isi  scopus
    5. Cheltsov I., Parka J., Shramov C., “Alpha-Invariants and Purely Log Terminal Blow-Ups”, Eur. J. Math., 4:3, 2, SI (2018), 845–858  crossref  mathscinet  isi  scopus
  • Математический сборник Sbornik: Mathematics (from 1967)
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