2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58876Let $X$ 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 $\frac{n-1}{n}$.Extended version, 14 pages, latexAlgebraic Geometry14J45, 14J70, 14E30text