Book Review
The AMS does not provide abstracts of book reviews.
You may download the entire review from the links below.
Full text of review:
PDF
This review is available free of charge.
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,
$34.95$
Shiro Goto, Koji Nishida, and Keiichi Watanabe, Non-Cohen-Macaulay symbolic blow-ups for space monomial curves and counterexamples to Cowsik’s question, Proc. Amer. Math. Soc. 120 (1994), no. 2, 383–392. MR 1163334, DOI 10.1090/S0002-9939-1994-1163334-9
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
J. Herzog, A. Simis, and W. V. Vasconcelos, On the arithmetic and homology of algebras of linear type, Trans. Amer. Math. Soc. 283 (1984), no. 2, 661–683. MR 737891, DOI 10.1090/S0002-9947-1984-0737891-6
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
Sam Huckaba and Craig Huneke, Rees algebras of ideals having small analytic deviation, Trans. Amer. Math. Soc. 339 (1993), no. 1, 373–402. MR 1123455, DOI 10.1090/S0002-9947-1993-1123455-7
Craig Huneke, The theory of $d$-sequences and powers of ideals, Adv. in Math. 46 (1982), no. 3, 249–279. MR 683201, DOI 10.1016/0001-8708(82)90045-7
Craig Huneke, On the symmetric and Rees algebra of an ideal generated by a $d$-sequence, J. Algebra 62 (1980), no. 2, 268–275. MR 563225, DOI 10.1016/0021-8693(80)90179-9
Joseph Lipman, Cohen-Macaulayness in graded algebras, Math. Res. Lett. 1 (1994), no. 2, 149–157. MR 1266753, DOI 10.4310/MRL.1994.v1.n2.a2
Artibano Micali, Sur les algèbres universelles, Ann. Inst. Fourier (Grenoble) 14 (1964), no. fasc. 2, 33–87 (French). MR 177009
Masayoshi Nagata, On the fourteenth problem of Hilbert, Proc. Internat. Congress Math. 1958., Cambridge Univ. Press, New York, 1960, pp. 459–462. MR 0116056
Sam Perlis, Maximal orders in rational cyclic algebras of composite degree, Trans. Amer. Math. Soc. 46 (1939), 82–96. MR 15, DOI 10.1090/S0002-9947-1939-0000015-X
D. Rees, On a problem of Zariski, Illinois J. Math. 2 (1958), 145–149. MR 95843
Paul 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), no. 2, 461–473. MR 1061491, DOI 10.1016/0021-8693(90)90141-A
- 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 -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 -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
DOI:
https://doi.org/10.1090/S0273-0979-97-00701-5
Review copyright:
© Copyright 1997
American Mathematical Society