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arXiv · 1710.04364

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

Burt Totaro
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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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Burt Totaro. 2017-10-12. The failure of Kodaira vanishing for Fano varieties, and terminal singularities that are not Cohen-Macaulay. https://arxiv.org/abs/1710.04364

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