Kawamata-Viehweg vanishing fails for log del Pezzo surfaces in characteristic 3 (1709.09238v3)

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.