Kawamata-Viehweg vanishing fails for log del Pezzo surfaces in characteristic 3

Abstract

We construct a klt del Pezzo surface in characteristic three violating the Kawamata-Viehweg vanishing theorem. As a consequence we show that there exists a Kawamata log terminal threefold singularity which is not Cohen-Macaulay in characteristic three.

arXiv comment21 pages, 2 figures. v3: presentation improved and fixed some typos. To appear in J. Pure Appl. Algebra