Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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



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

Authors: Mark R. Johnson and K. N. Raghavan
Journal: Proc. Amer. Math. Soc. 123 (1995), 1991-1994
MSC: Primary 13A30; Secondary 13F50, 13H10
MathSciNet review: 1264817
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [BST] W. Bruns, A. Simis, and N. V. Trung, Blow-up of straightening-closed ideals in ordinal hodge algebras, Trans. Amer. Math. Soc. 326 (1991), 507-528. MR 1005076 (91k:13004)
  • [EH] D. Eisenbud and C. Huneke, Cohen-Macaulay Rees algebras and their specializations, J. Algebra 81 (1983), 202-224. MR 696134 (84h:13030)
  • [HSV] J. Herzog, A. Simis, and W. V. Vasconcelos, Koszul homology and blowing up rings, Lecture Notes in Pure and Appl. Math., vol. 84, Marcel Dekker, New York, 1983, pp. 79-169. MR 686942 (84k:13015)
  • [HH] S. Huckaba and C. Huneke, Powers of ideals having small analytic deviation, Amer. J. Math. 114 (1992), 367-403. MR 1156570 (93g:13002)
  • [H1] C. Huneke, Symbolic powers of prime ideals and special graded algebras, Comm. Algebra 9 (1981), 339-366. MR 605026 (83a:13011)
  • [H2] -, Powers of ideals generated by weak d-sequences, J. Algebra 68 (1981), 471-509. MR 608547 (82k:13003)
  • [HTU] J. Herzog, N. V. Trung, and B. Ulrich, On the multiplicity of blow-up rings of ideals generated by d-seduences, J. Pure Appl. Algebra 80 (1992), 273-297. MR 1170714 (93h:13004)
  • [MS] M. Morales and A. Simis, Symbolic powers of monomial curves in $ {{\text{P}}_3}$ lying on $ xw - yz = 0$, Comm. Algebra 20 (1992), 1109-1121. MR 1154405 (93c:13005)
  • [R] K. Raghavan, Powers of ideals generated by quadratic sequences, Trans. Amer. Math. Soc. 343 (1994), 727-747. MR 1188639 (94i:13007)
  • [RS] K. Raghavan and A. Simis, Multiplicities of blow-ups of homogeneous quadratic sequences, preprint.
  • [S] P. Schenzel, Examples of Gorenstein domains and symbolic powers of monomial space curves, J. Pure Appl. Algebra 71 (1991), 297-311. MR 1117640 (92h:13021)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 13A30, 13F50, 13H10

Retrieve articles in all journals with MSC: 13A30, 13F50, 13H10

Additional Information

Article copyright: © Copyright 1995 American Mathematical Society

American Mathematical Society