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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Determinantal varieties, monomial semigroups, and algebras associated with ideals


Author: Jacob Barshay
Journal: Proc. Amer. Math. Soc. 40 (1973), 16-22
MSC: Primary 13H10; Secondary 14M05
DOI: https://doi.org/10.1090/S0002-9939-1973-0318137-8
MathSciNet review: 0318137
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Abstract: This paper is concerned with the Rees and symmetric algebras of powers of ideals generated by $ A$-sequences. These algebras are represented as quotients of polynomial rings over $ A$ by ideals defined by minors of matrices. Their Krull dimensions are computed when $ A$ is a finite domain over a field. When $ A$ is a polynomial ring over a Cohen-Macaulay ring $ {A_0}$ and the $ A$-sequence consists of indeterminates, the Rees algebra is shown to be Cohen-Macaulay. If furthermore $ {A_0}$ is a finite domain over a field, the symmetric algebra is shown to be Cohen-Macaulay only for $ A$-sequences and squares of $ A$-sequences of length two. Connections with algebras generated by monomials and Veronese varieties are pointed out.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0318137-8
Keywords: Rees algebra, symmetric algebra, Cohen-Macaulay ring, perfect ideal, determinantal ideal, normal monomial semigroup, Veronese variety
Article copyright: © Copyright 1973 American Mathematical Society