Communications in Contemporary Mathematics ( IF 1.278 ) Pub Date : 2020-09-15 , DOI: 10.1142/s021919972050039x
Joaquín Moraga; Jinhyung Park; Lei Song

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 $reg(𝒪X)≤d−e$, 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.

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