Total log canonical thresholds and generalized Eckardt points

Abstract

Let X be a smooth hypersurface of degree n greater than or equal to 3 in 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 of X is (n - 1)/n if and only if H is a cone in Pn-1 over a smooth hypersurface of degree n in Pn-2.