Cohen-Macaulayness of blow-ups of homogeneous weak 𝑑-sequences

Johnson, Mark R.; Raghavan, K. N.

doi:10.1090/S0002-9939-1995-1264817-4

Cohen-Macaulayness of blow-ups of homogeneous weak $d$-sequences
HTML articles powered by AMS MathViewer

by Mark R. Johnson and K. N. Raghavan

Proc. Amer. Math. Soc. 123 (1995), 1991-1994

DOI: https://doi.org/10.1090/S0002-9939-1995-1264817-4

PDF | Request permission

Abstract:

Let R be a homogeneous Cohen-Macaulay algebra over a field, and let I be an ideal generated by a homogeneous weak d-sequence. We show, under reasonable conditions on the sequence, that the graded ring ${\text {gr}_M}R[It]$ of the Rees algebra $R[It] = { \oplus _{i \geq 0}}{I^i}$ is Cohen-Macaulay. In particular we obtain the Cohen-Macaulayness of the blow-up ring $R[It]$.

References

Winfried Bruns, Aron Simis, and Ngô Việt Trung, Blow-up of straightening-closed ideals in ordinal Hodge algebras, Trans. Amer. Math. Soc. 326 (1991), no. 2, 507–528. MR 1005076, DOI 10.1090/S0002-9947-1991-1005076-8
David Eisenbud and Craig Huneke, Cohen-Macaulay Rees algebras and their specialization, J. Algebra 81 (1983), no. 1, 202–224. MR 696134, DOI 10.1016/0021-8693(83)90216-8
J. Herzog, A. Simis, and W. V. Vasconcelos, Koszul homology and blowing-up rings, Commutative algebra (Trento, 1981) Lecture Notes in Pure and Appl. Math., vol. 84, Dekker, New York, 1983, pp. 79–169. MR 686942
Sam Huckaba and Craig Huneke, Powers of ideals having small analytic deviation, Amer. J. Math. 114 (1992), no. 2, 367–403. MR 1156570, DOI 10.2307/2374708
Craig Huneke, Symbolic powers of prime ideals and special graded algebras, Comm. Algebra 9 (1981), no. 4, 339–366. MR 605026, DOI 10.1080/00927878108822586
Craig Huneke, Powers of ideals generated by weak $d$-sequences, J. Algebra 68 (1981), no. 2, 471–509. MR 608547, DOI 10.1016/0021-8693(81)90276-3
Jürgen Herzog, Ngô Viêt Trung, and Bernd Ulrich, On the multiplicity of blow-up rings of ideals generated by $d$-sequences, J. Pure Appl. Algebra 80 (1992), no. 3, 273–297. MR 1170714, DOI 10.1016/0022-4049(92)90146-7
Marcel Morales and Aron Simis, Symbolic powers of monomial curves in $\textbf {P}^3$ lying on a quadric surface, Comm. Algebra 20 (1992), no. 4, 1109–1121. MR 1154405, DOI 10.1080/00927879208824394
K. Raghavan, Powers of ideals generated by quadratic sequences, Trans. Amer. Math. Soc. 343 (1994), no. 2, 727–747. MR 1188639, DOI 10.1090/S0002-9947-1994-1188639-1

Multiplicities of blow-ups of homogeneous quadratic sequences

Peter Schenzel, Examples of Gorenstein domains and symbolic powers of monomial space curves, J. Pure Appl. Algebra 71 (1991), no. 2-3, 297–311. MR 1117640, DOI 10.1016/0022-4049(91)90153-S