Vanishing Theorem for Hodge Ideals on smooth hypersurfaces

Abstract

We use a Koszul-type resolution to prove a weak version of Bott's vanishing theorem for smooth hypersurfaces in P n and use this result to prove a vanishing theorem for Hodge ideals associated to an effective Cartier divisor on a hypersurface. This extends an earlier result of Mustat ¸ȃ and Popa.