Regularity of structure sheaves of varieties with isolated singularities

Joaquín Moraga, Jinhyung Park, Lei Song

Research output: Contribution to journalArticlepeer-review

Abstract

Let X PN 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(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.

Original languageEnglish (US)
Article number2050039
JournalCommunications in Contemporary Mathematics
DOIs
StateAccepted/In press - 2020

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Keywords

  • Castelnuovo-Mumford regularity
  • Eisenbud-Goto regularity conjecture
  • double point divisor
  • isolated singularity
  • multiplier ideal

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