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Rees Algebras of Powers of Maximal Graded Ideals

Volume 9, Number 1 (2010), 31 - 35

Rees Algebras of Powers of Maximal Graded Ideals

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Abstract

We give the cohomology groups of the Rees algebra R 0 of the s-th power of the maximal graded ideal m=(x1; : : : ;xn) of the quotient ring A=B=J, B=K[X1; : : : ;Xn], K field, J graded ideal, in terms of the corresponding cohomology modules of the Rees algebra of A. As applications, we compute the depth of R 0 and we give an upper bound for its regularity.