Determinantal varieties, monomial semigroups, and algebras associated with ideals
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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.References
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Additional Information
- © Copyright 1973 American Mathematical Society
- 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