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Mat. Sb., 2002, Volume 193, Number 5, Pages 149–160 (Mi msb656)  

This article is cited in 19 scientific papers (total in 19 papers)

Total log canonical thresholds and generalized Eckardt points

I. A. Cheltsova, J. Parkb

a University of Liverpool
b University of Georgia

Abstract: Let $X$ be a smooth hypersurface of degree $n\geqslant 3$ in ${\mathbb P}^n$. It is proved that the log canonical threshold of an arbitrary hyperplane section $H$ of it is at least $(n-1)/n$. Under the assumption of the log minimal model program it is also proved that the log canonical threshold of $H\subset X$ is $(n-1)/n$ if and only if $H$ is a cone in ${\mathbb P}^{n-1}$ over a smooth hypersurface of degree $n$ in ${\mathbb P}^{n-2}$.


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English version:
Sbornik: Mathematics, 2002, 193:5, 779–789

Bibliographic databases:

UDC: 513.6
MSC: 14J17
Received: 31.05.2001

Citation: I. A. Cheltsov, J. Park, “Total log canonical thresholds and generalized Eckardt points”, Mat. Sb., 193:5 (2002), 149–160; Sb. Math., 193:5 (2002), 779–789

Citation in format AMSBIB
\by I.~A.~Cheltsov, J.~Park
\paper Total log canonical thresholds and generalized Eckardt points
\jour Mat. Sb.
\yr 2002
\vol 193
\issue 5
\pages 149--160
\jour Sb. Math.
\yr 2002
\vol 193
\issue 5
\pages 779--789

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    This publication is cited in the following articles:
    1. de Fernex T., Ein L., Mustaţă M., “Bounds for log canonical thresholds with applications to birational rigidity”, Math. Res. Lett., 10:2-3 (2003), 219–236  mathscinet  zmath  isi  elib
    2. A. V. Pukhlikov, “Birationally rigid iterated Fano double covers”, Izv. Math., 67:3 (2003), 555–596  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. McKernan J., Prokhorov Yu., “Threefold thresholds”, Manuscripta Math., 114:3 (2004), 281–304  crossref  mathscinet  zmath  isi  elib  scopus
    4. I. A. Cheltsov, “Birationally superrigid cyclic triple spaces”, Izv. Math., 68:6 (2004), 1229–1275  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. I. A. Cheltsov, “Birationally rigid Fano varieties”, Russian Math. Surveys, 60:5 (2005), 875–965  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    6. 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
    7. Cools F., Coppens M., “Star points on smooth hypersurfaces”, J. Algebra, 323:1 (2010), 261–286  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    8. Birkar C., Shokurov V.V, “Mld's vs thresholds and flips”, Journal fur Die Reine und Angewandte Mathematik, 638 (2010), 209–234  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    9. Munteanu O., Szekelyhidi G., “On convergence of the Kahler-Ricci flow”, Comm Anal Geom, 19:5 (2011), 887–903  crossref  mathscinet  isi  scopus  scopus  scopus
    10. Ivan Cheltsov, Jihun Park, Joonyeong Won, “Log canonical thresholds of certain Fano hypersurfaces”, Math. Z, 2013  crossref  mathscinet  isi  scopus  scopus
    11. 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
    12. 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
    13. 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
    14. Szekelyhidi G., “Kahler-Einstein Metrics”, Modern Geometry: a Celebration of the Work of Simon Donaldson, Proceedings of Symposia in Pure Mathematics, 99, eds. Munoz V., Smith I., Thomas R., Amer Chemical Soc, 2018, 331–361  crossref  mathscinet  isi
    15. Park J., Won J., “K-Stability of Smooth Del Pezzo Surfaces”, Math. Ann., 372:3-4 (2018), 1239–1276  crossref  mathscinet  zmath  isi  scopus
    16. 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
    17. Liu Yu., Xu Ch., “K-Stability of Cubic Threefolds”, Duke Math. J., 168:11 (2019), 2029–2073  crossref  mathscinet  zmath  isi
    18. 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
    19. Stibitz Ch. Zhuang Z., “Birational Superrigidity and K-Stability of Fano Complete Intersections of Index 1”, Duke Math. J., 169:12 (2020), 2205–2229  crossref  mathscinet  isi
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