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

By B. Totaro. Journal of Algebraic Geometry, 2017

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We show that the Kodaira vanishing theorem can fail on smooth Fano varieties of any characteristic p > 0 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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/401ffc87a0dde7cf354637f24b7844dad5ef0d85