Log Canonical Thresholds and Generalized Eckardt Points

Ivan Cheltsov, Jihun Park

Let $X$ be a smooth hypersurface of degree $n\ge 3$ 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…