Bulletin of the American Mathematical Society

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Book Information:

Author: V. L. Popov
Title: Groups, generators, syzygies, and orbits in invariant theory
Additional book information: (translated from the Russian by A. Martsinkovsky). Translations of Mathematical Monographs, vol. 100, American Mathematical Society, Providence, RI, 1992, vi + 245 pp., US$181.00. ISBN 0-8218-4557-8.

N. L. Gordeev, Coranks of elements of linear groups and the complexity of algebras of invariants, Algebra i Analiz 2 (1990), no. 2, 39–64 (Russian); English transl., Leningrad Math. J. 2 (1991), no. 2, 245–267. MR 1062262

Melvin Hochster and Joel L. Roberts, Rings of invariants of reductive groups acting on regular rings are Cohen-Macaulay, Advances in Math. 13 (1974), 115–175. MR 347810, DOI 10.1016/0001-8708(74)90067-X

George Kempf, The Hochster-Roberts theorem of invariant theory, Michigan Math. J. 26 (1979), no. 1, 19–32. MR 514958

Friedrich Knop, Über die Glattheit von Quotientenabbildungen, Manuscripta Math. 56 (1986), no. 4, 419–427 (German, with English summary). MR 860731, DOI 10.1007/BF01168503

M. Pavaman Murthy, A note on factorial rings, Arch. Math. (Basel) 15 (1964), 418–420. MR 173695, DOI 10.1007/BF01589225

D. I. Panyushev, Regular elements in spaces of linear representations. II, Izv. Akad. Nauk SSSR Ser. Mat. 49 (1985), no. 5, 979–985, 1120 (Russian). MR 810527

Richard P. Stanley, Hilbert functions of graded algebras, Advances in Math. 28 (1978), no. 1, 57–83. MR 485835, DOI 10.1016/0001-8708(78)90045-2

Richard P. Stanley, Combinatorics and invariant theory, Relations between combinatorics and other parts of mathematics (Proc. Sympos. Pure Math., Ohio State Univ., Columbus, Ohio, 1978) Proc. Sympos. Pure Math., XXXIV, Amer. Math. Soc., Providence, R.I., 1979, pp. 345–355. MR 525334

[Go]

N. L. Gordeev, Coranks of elements of linear groups, and complexity of algebras of invariants, Leningrad Math. J. 2 (1991), 245-267. MR 1062262 (91h:20063)

[HR]

M. Hochster and J. Roberts, Rings of invariants of reductive groups acting on regular rings are Cohen-Macaulay, Adv. Math. 13 (1974), 125-175. MR 0347810 (50:311)

[Ke]

G. Kempf, The Hochster-Roberts theorem in invariant theory, Michigan Math. J. 26 (1979), 19-32. MR 514958 (80g:14040)

[Kn]

F. Knop, Über die Glattheit von Quotientenabbildungen, Manuscripta Math. 56 (1986), 419-426. MR 860731 (88f:14041)

[Mu]

M. P. Murthy, A note on factorial rings, Arch. Math. 15 (1964), 418-420. MR 0173695 (30:3905)

[Pa]

D. I. Panyushev, Regular elements in spaces of linear representations. II, Math. USSR-Izv. 27 (1986), 279-284. MR 810527 (87c:14011)

[St1]

R. P. Stanley, Hilbert functions of graded algebras, Adv. Math. 28 (1978), 57-83. MR 0485835 (58:5637)

[St2]

-, Combinatorics and invariant theory, Proc. Sympos. Pure. Math., vol. 34, Amer. Math. Soc., Providence, RI, 1979, pp. 345-355. MR 525334 (80e:15020)