The arithmetic Cohen-Macaulay character of schubert schemes
1972; Mittag-Leffler Institute; Volume: 129; Linguagem: Inglês
10.1007/bf02392211
ISSN1871-2509
Autores Tópico(s)Commutative Algebra and Its Applications
ResumoIn this paper we prove the following theorem.(For the notation, see Section 2.) Trrv, oR~l~ 1.Let R be a Cohen-Macaulay ring.Then then homogenous coordinate ring ol the Schubert scheme ~(al.. . as) is Cohen-Macaulay o/relative dimensionThe theorem was also proved by M. Hochster.For an announcement of his results, see [5].It was proved in a weaker local case (see Theorem 12 below) by J. A. Eagon and M. Hochster in "Cohen-Macaulay rings, invariant theory and the generic perfection of determinental loci" (to appear, cf.[3]).The proof below owes many of its ideas to Eagon and Hochster and to G. Kempf.Frequent discussions with S. Kleiman and T. Svanes have also been helpful.I am especially grateful to Kleiman for his patient help preparing this
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