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.
Initial algebras of Pfaffian rings
DE NEGRI, EMANUELA;
2013-01-01
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.
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