Log Canonical Thresholds and Generalized Eckardt Points

Details Log Canonical Thresholds and Generalized Eckardt Points Log Canonical Thresholds and Generalized Eckardt Points

2000-03-20

arxiv.org/abs/math/0003121v2

Mathematics

Algebraic Geometry

Extended version, 14 pages, latex

Scientific paper

Let $X$ be a smooth hypersurface of degree $n\geq 3$ in $\mathbb{P}^n$. We prove that the log canonical threshold of $H\in|-K_X|$ is at least $\frac{n-1}{n}$. Under the assumption of the Log minimal model program, we also prove that a hyperplane section $H$ of $X$ is a cone in $\mathbb{P}^{n-1}$ over a smooth hypersurface of degree $n$ in $\mathbb{P}^{n-2}$ if and only if the log canonical threshold of $H$ is $\frac{n-1}{n}$.

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