CohenMacaulay rings and ideal theory in rings of invariants of algebraic groups
Author:
Ronald E. Kutz
Journal:
Trans. Amer. Math. Soc. 194 (1974), 115129
MSC:
Primary 13C15; Secondary 13H10, 14M15, 15A72, 20G15
MathSciNet review:
0352082
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Abstract: Theorem. Let R be a commutative Noetherian ring with identity. Let M = be an s by s symmetric matrix with entries in R. Let I the be ideal of by minors of M. Suppose that the grade of I is as large as possible, namely, gr . Then I is a perfect ideal, so that is Cohen Macaulay if R is. Let G be a linear algebraic group acting rationally on . Hochster has conjectured that if G is reductive, then is CohenMacaulay, where denotes the ring of invariants of the action of G. The above theorem provides a special case of this conjecture. For , the orthogonal group, and K a field of characteristic zero, the above yields: Corollary. For R and G as above, is CohenMacaulay for an appropriate action of G. In order to obtain these results it was necessary to prove a more general form of the theorem stated above, which in turn yields a more general form of the corollary.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947197403520822
PII:
S 00029947(1974)03520822
Keywords:
CohenMacaulay rings,
ideals generated by minors of matrices,
perfectideals,
rings of invariants,
orthogonal group
Article copyright:
© Copyright 1974
American Mathematical Society
