The failure of Kodaira vanishing for Fano varieties, and terminal singularities that are not Cohen-Macaulay

Totaro, Burt

doi:10.1090/jag/724

Author: Burt Totaro
Journal: J. Algebraic Geom. 28 (2019), 751-771
DOI: https://doi.org/10.1090/jag/724
Published electronically: June 7, 2019
MathSciNet review: 3994312
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Abstract | References | Additional Information

Abstract: We show that the Kodaira vanishing theorem can fail on smooth Fano varieties of any characteristic $p>0$. Taking cones over some of these varieties, we give the first examples of terminal singularities which are not Cohen-Macaulay. By a different method, we construct a terminal singularity of dimension 3 (the lowest possible) in characteristic 2 which is not Cohen-Macaulay.

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Additional Information

Burt Totaro
Affiliation: Department of Mathematics, University of California Los Angeles, Box 951555, Los Angeles, California 90095-1555
MR Author ID: 272212
Email: totaro@math.ucla.edu

Received by editor(s): October 17, 2017
Received by editor(s) in revised form: March 21, 2018
Published electronically: June 7, 2019
Additional Notes: This work was supported by NSF grant DMS-1701237.
Article copyright: © Copyright 2019 University Press, Inc.