Regularity of structure sheaves of varieties with isolated singularities

Joaquín Moraga, Jinhyung Park, Lei Song

Research output: Contribution to journalArticlepeer-review


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
StateAccepted/In press - 2020

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics


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

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