Geodesic
Total log canonical thresholds and generalized Eckardt points
Sbornik. Mathematics, Tome 193 (2002) no. 5, pp. 779-789 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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     author = {I. A. Cheltsov and J. Park},
     title = {Total log canonical thresholds and generalized {Eckardt} points},
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     volume = {193},
     number = {5},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2002_193_5_a8/}
}
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I. A. Cheltsov; J. Park. Total log canonical thresholds and generalized Eckardt points. Sbornik. Mathematics, Tome 193 (2002) no. 5, pp. 779-789. http://geodesic.mathdoc.fr/item/SM_2002_193_5_a8/

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