Regularity of structure sheaves of varieties with isolated singularities

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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.
Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
Issue Date
2021-08
Language
English
Article Type
Article
Citation

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, v.23, no.05

ISSN
0219-1997
DOI
10.1142/S021919972050039X
URI
http://hdl.handle.net/10203/295152
Appears in Collection
MA-Journal Papers(저널논문)
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