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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2009, Volume 264, Pages 37–51 (Mi tm805)  
This article is cited in 12 scientific papers (total in 12 papers)

Extremal Metrics on del Pezzo Threefolds

I. A. Cheltsov, K. A. Shramov

School of Mathematics, University of Edinburgh, Edinburgh, UK
Full-text PDF (253 kB) Citations (12)
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Abstract: We prove the existence of Kähler–Einstein metrics on a nonsingular section of the Grassmannian Gr(2,5)⊂P9 by a linear subspace of codimension 3 and on the Fermat hypersurface of degree 6 in P(1,1,1,2,3). We also show that a global log canonical threshold of the Mukai–Umemura variety is equal to 1/2.
Received in August 2008
English version:
Proceedings of the Steklov Institute of Mathematics, 2009, Volume 264, Pages 30–44
DOI: https://doi.org/10.1134/S0081543809010040
Bibliographic databases:
Document Type: Article
UDC: 512.7
Language: Russian
Citation: I. A. Cheltsov, K. A. Shramov, “Extremal Metrics on del Pezzo Threefolds”, Multidimensional algebraic geometry, Collected papers. Dedicated to the Memory of Vasilii Alekseevich Iskovskikh, Corresponding Member of the Russian Academy of Sciences, Trudy Mat. Inst. Steklova, 264, MAIK Nauka/Interperiodica, Moscow, 2009, 37–51; Proc. Steklov Inst. Math., 264 (2009), 30–44
Citation in format AMSBIB
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\by I.~A.~Cheltsov, K.~A.~Shramov
\paper Extremal Metrics on del Pezzo Threefolds
\inbook Multidimensional algebraic geometry
\bookinfo Collected papers. Dedicated to the Memory of Vasilii Alekseevich Iskovskikh, Corresponding Member of the Russian Academy of Sciences
\serial Trudy Mat. Inst. Steklova
\yr 2009
\vol 264
\pages 37--51
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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Linking options:
  • https://www.mathnet.ru/eng/tm805
  • https://www.mathnet.ru/eng/tm/v264/p37
    • This publication is cited in the following 12 articles:
    1. Charles P. Boyer, Hongnian Huang, Eveline Legendre, Christina W. Tønnesen-Friedman, “Existence and non-existence of constant scalar curvature and extremal Sasaki metrics”, Math. Z., 304:4 (2023)  crossref
    2. Ivan Cheltsov, Constantin Shramov, “Kähler–Einstein Fano threefolds of degree 22”, J. Algebraic Geom., 32 (2023), 385–428  mathnet  crossref
    3. Cheltsov I., Park J., Prokhorov Yu., Zaidenberg M., “Cylinders in Fano Varieties”, EMS Surv. Math. Sci., 8:1-2 (2021), 39–105  crossref  mathscinet  isi
    4. Xu Ch., “K-Stability of Fano Varieties: An Algebro-Geometric Approach”, EMS Surv. Math. Sci., 8:1-2 (2021), 265–354  crossref  mathscinet  isi
    5. Golota A., “Delta-Invariants For Fano Varieties With Large Automorphism Groups”, Int. J. Math., 31:10 (2020), 2050077  crossref  mathscinet  isi
    6. Cheltsov I.A., Rubinstein Ya.A., Zhang K., “Basis Log Canonical Thresholds, Local Intersection Estimates, and Asymptotically Log Del Pezzo Surfaces”, Sel. Math.-New Ser., 25:2 (2019), UNSP 34  crossref  mathscinet  isi  scopus
    7. V. V. Przyjalkowski, I. A. Cheltsov, K. A. Shramov, “Fano threefolds with infinite automorphism groups”, Izv. Math., 83:4 (2019), 860–907  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    8. Chung K., Hong J., Lee S., “Geometry of Moduli Spaces of Rational Curves in Linear Sections of Grassmannian Gr(2,5)”, J. Pure Appl. Algebr., 222:4 (2018), 868–888  crossref  mathscinet  zmath  isi  scopus
    9. Sławomir Dinew, Grzegorz Kapustka, Michał Kapustka, “Remarks on Mukai threefolds admitting C∗ action”, Mosc. Math. J., 17:1 (2017), 15–33  mathnet  crossref  mathscinet
    10. Fujita K., “Examples of K-Unstable Fano Manifolds With the Picard Number 1”, Proc. Edinb. Math. Soc., 60:4 (2017), 881–891  crossref  mathscinet  zmath  isi  scopus
    11. Cremona Groups and the Icosahedron, 2015, 438  crossref
    12. Odaka Yu., Sano Yu., “Alpha invariant and K-stability of Q-Fano varieties”, Adv Math, 229:5 (2012), 2818–2834  crossref  mathscinet  zmath  isi  elib  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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