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Book Review

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Book Information:

Author: Wolmer V. Vasconcelos
Title: Arithmetic of blowup algebras
Additional book information: London Math. Soc. Lecture Note Ser., vol. 195 Cambridge Univ. Press, Cambridge, 1994, 329 pp., ISBN 0-521-45484-0, $34.95

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

  • 1. S. Goto, K. Nishida, and K. Watanabe, Non-Cohen-Macaulay symbolic blow-ups for space monomial curves and counterexamples to Cowsik's question, Proc. Amer. Math. Soc. 120 (1994), 383-392. MR 94d:13005
  • 2. J. Herzog, A. Simis, and W. V. Vasconcelos, Koszul homology and blowing-up rings, Commutative Algebra, Proceedings: Trento 1981 (S. Greco and G. Valla, eds.), Lecture Notes Pure Appl. Math., vol. 84, Marcel Dekker, New York, 1983, pp. 79-169. MR 84k:13015
  • 3. -, On the arithmetic and homology of algebras of linear type, Trans. Amer. Math. Soc. 283 (1984), 661-683. MR 86a:13015
  • 4. S. Huckaba and C. Huneke, Powers of ideals having small analytic deviation, Amer. J. Math. 114 (1992), 367-403. MR 93g:13002
  • 5. -, Rees algebras of ideals having small analytic deviation, Trans. Amer. Math. Soc. 339 (1993), 373-402. MR 93k:13008
  • 6. C. Huneke, The theory of $d$-sequences and powers of ideals, Adv. in Math. 46 (1982), 249-279. MR 84g:13021
  • 7. -, On the symmetric and Rees algebras of an ideal generated by a $d$-sequence, J. Algebra 62 (1980), 268-275. MR 81d:13016
  • 8. J. Lipman, Cohen-Macaulayness in graded algebras, Math. Res. Lett. 1 (1994), 149-157. MR 95d:13006
  • 9. A. Micali, Sur les algèbres universelles, Ann. Inst. Fourier 14 (1964), 33-88. MR 31:1275
  • 10. M. Nagata, On the fourteenth problem of Hilbert, Proceedings of the International Congress of Mathematicians, 1958, Cambridge Univ. Press, London, 1960, pp. 459-462. MR 22:6851
  • 11. D. G. Northcott and D. Rees, Reductions of ideals in local rings, Proc. Cambridge Philos. Soc. 50 (1954), 145-158. MR 15:596a
  • 12. D. Rees, On a problem of Zariski, Illinois J. Math. 2 (1958), 145-149. MR 20:2341
  • 13. P. Roberts, An infinitely generated symbolic blow-up in a power series ring and a new counterexample to Hilbert's Fourteenth Problem, J. Algebra 132 (1990), 461-473. MR 91j:13006

Review Information:

Reviewer: Bernd Ulrich
Affiliation: Michigan State University
Email: ulrich@math.msu.edu
Journal: Bull. Amer. Math. Soc. 34 (1997), 177-181
MSC (1991): Primary 13A30; Secondary 13-02, 13C20, 13C40, 13D02, 13D40, 13F15, 13H10, 13P10
DOI: https://doi.org/10.1090/S0273-0979-97-00701-5
Review copyright: © Copyright 1997 American Mathematical Society
American Mathematical Society