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Mat. Sb., 2001, Volume 192, Number 8, Pages 155–172 (Mi msb591)  

This article is cited in 26 scientific papers (total in 26 papers)

Log canonical thresholds on hypersurfaces

I. A. Cheltsov


Abstract: A lower bound for global log canonical thresholds on smooth hypersurfaces is found. This bound cannot be improved for the fixed degree and dimension of the hypersurface.

DOI: https://doi.org/10.4213/sm591

Full text: PDF file (285 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2001, 192:8, 1241–1257

Bibliographic databases:

UDC: 513.6
MSC: Primary 14J17; Secondary 14B05, 14E30
Received: 26.12.2000

Citation: I. A. Cheltsov, “Log canonical thresholds on hypersurfaces”, Mat. Sb., 192:8 (2001), 155–172; Sb. Math., 192:8 (2001), 1241–1257

Citation in format AMSBIB
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\paper Log canonical thresholds on hypersurfaces
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Viswanathan N., “Lowest Log Canonical Thresholds of a Reduced Plane Curve of Degree D”, Eur. J. Math.  crossref  isi
    2. A. V. Pukhlikov, “Birationally rigid Fano hypersurfaces”, Izv. Math., 66:6 (2002), 1243–1269  mathnet  crossref  crossref  mathscinet  zmath
    3. A. V. Pukhlikov, “Birationally rigid Fano hypersurfaces with isolated singularities”, Sb. Math., 193:3 (2002), 445–471  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. A. V. Pukhlikov, “Birationally rigid iterated Fano double covers”, Izv. Math., 67:3 (2003), 555–596  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. I. A. Cheltsov, “Birationally superrigid cyclic triple spaces”, Izv. Math., 68:6 (2004), 1229–1275  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. McKernan J., Prokhorov Yu., “Threefold thresholds”, Manuscripta Math., 114:3 (2004), 281–304  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    7. I. A. Cheltsov, “Birationally rigid Fano varieties”, Russian Math. Surveys, 60:5 (2005), 875–965  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    8. I. A. Cheltsov, “Local inequalities and birational superrigidity of Fano varieties”, Izv. Math., 70:3 (2006), 605–639  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    9. Hwang Jun-Muk, “Log canonical thresholds of divisors on Grassmannians”, Math. Ann., 334:2 (2006), 413–418  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    10. I. A. Cheltsov, K. A. Shramov, “Log canonical thresholds of smooth Fano threefolds”, Russian Math. Surveys, 63:5 (2008), 859–958  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    11. Cheltsov I., “Log canonical thresholds of del Pezzo surfaces”, Geom. Funct. Anal., 18:4 (2008), 1118–1144  crossref  mathscinet  zmath  isi  scopus  scopus
    12. I. A. Cheltsov, “Extremal metrics on two Fano varieties”, Sb. Math., 200:1 (2009), 95–132  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    13. 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
    14. A. V. Pukhlikov, “Birational Geometry of Singular Fano Varieties”, Proc. Steklov Inst. Math., 264 (2009), 159–177  mathnet  crossref  mathscinet  isi  elib  elib
    15. A. V. Pukhlikov, “Birationally rigid varieties. II. Fano fibre spaces”, Russian Math. Surveys, 65:6 (2010), 1083–1171  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    16. Shi Ya., “On the alpha-invariants of cubic surfaces with Eckardt points”, Advances in Mathematics, 225:3 (2010), 1285–1307  crossref  mathscinet  zmath  isi  scopus
    17. Ivan Cheltsov, Dimitra Kosta, “Computing α-Invariants of Singular del Pezzo Surfaces”, J Geom Anal, 2012  crossref  mathscinet  isi  scopus  scopus  scopus
    18. Ivan Cheltsov, Jihun Park, Joonyeong Won, “Log canonical thresholds of certain Fano hypersurfaces”, Math. Z, 2013  crossref  mathscinet  isi  scopus  scopus  scopus
    19. A. V. Pukhlikov, “Birational geometry of higher-dimensional Fano varieties”, Proc. Steklov Inst. Math., 288, suppl. 2 (2015), S1–S150  mathnet  crossref  crossref  isi  elib
    20. Cheltsov I. Park J. Won J., “Affine cones over smooth cubic surfaces”, J. Eur. Math. Soc., 18:7 (2016), 1537–1564  crossref  mathscinet  zmath  isi  scopus
    21. Cheltsov I., “Worst Singularities of Plane Curves of Given Degree”, J. Geom. Anal., 27:3 (2017), 2302–2338  crossref  mathscinet  zmath  isi  scopus
    22. 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
    23. 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  zmath  isi  scopus
    24. 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
    25. Stibitz Ch., Zhuang Z., “K-Stability of Birationally Superrigid Fano Varieties”, Compos. Math., 155:9 (2019), 1845–1852  crossref  mathscinet  zmath  isi
    26. Fujita K., “K-Stability of Fano Manifolds With Not Small Alpha Invariants”, J. Inst. Math. Jussieu, 18:3 (2019), 519–530  crossref  mathscinet  zmath  isi
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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