Regularity of structure sheaves of varieties with isolated singularities

Abstract

Let X subset of P-N be a non-degenerate normal projective variety of codimension e and degree d with isolated Q-Gorenstein singularities. We prove that the Castelnuovo-Mumford regularity reg(O-X) <= d - e, as predicted by the Eisenbud-Goto regularity conjecture. Such a bound fails for general projective varieties by a recent result of McCullough-Peeva. The main techniques are Noma's classification of non-degenerate projective varieties and Nadel vanishing for multiplier ideals. We also classify the extremal and the next to extremal cases.