Regularity of structure sheaves of varieties with isolated singularities

2018/08/29 by Moraga, Joaquín, Park, Jinhyung, Song, Lei
#Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1808.09713

Abstract

Let X⊆ 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. The main techniques are Noma's classification of non-degenerated projective varieties and Nadel vanishing for multiplier ideals. We also classify the extremal and the next to extremal cases.

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