INITIAL ALGEBRAS OF PFAFFIAN RINGS

Abstract

We compute initial algebras of standard Pfaffian rings via suitable embeddings. This yields simple proofs that these rings are normal Gorenstein domains, with rational singularities in characteristic 0 and F-rational in characteristic p > 0. We also determine their a-invariants. These methods can also be applied to prove the same properties for rings defined by cogenerated Pfaffian ideals.