The Michigan Mathematical Journal

Frobenius splitting of certain rings of invariants

V. Lakshmibai, K. N. Raghavan, and P. Sankaran

Source: Michigan Math. J. Volume 57 (2008), 499-510.

Primary Subjects: 20G05, 20G10, 17B10
Secondary Subjects: 17B20, 17B45, 14F05

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.
If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.mmj/1220879421
Digital Object Identifier: doi:10.1307/mmj/1220879421
Mathematical Reviews number (MathSciNet): MR2492465
Zentralblatt MATH identifier: 05604544

References

M. Brion and S. Kumar, Frobenius splitting methods in geometry and representation theory, Progr. Math., 231, Birkhäuser, Boston, 2005.
Mathematical Reviews (MathSciNet): MR2107324
Zentralblatt MATH: 1072.14066
C. De Concini and C. Procesi A characteristic-free approach to invariant theory, Adv. Math. 21 (1976), 330--354.
Mathematical Reviews (MathSciNet): MR422314
Digital Object Identifier: doi:10.1016/S0001-8708(76)80003-5
N. Hara and K.-i. Watanabe, $F$-regular and $F$-pure rings vs. log terminal and log canonical singularities, J. Algebraic Geom. 11 (2002), 363--392.
Mathematical Reviews (MathSciNet): MR1874118
M. Hashimoto, Good filtrations of symmetric algebras and strong $F$-regularity of invariant subrings, Math. Z. 236 (2001), 605--623.
Mathematical Reviews (MathSciNet): MR1821307
Digital Object Identifier: doi:10.1007/PL00004844
M. Hochster and J. L. Roberts, Rings of invariants of reductive groups acting on regular rings are Cohen--Macaulay, Adv. Math. 13 (1974), 115--175.
Mathematical Reviews (MathSciNet): MR347810
Digital Object Identifier: doi:10.1016/0001-8708(74)90067-X
------, The purity of the Frobenius and local cohomology, Adv. Math. 21 (1976), 117--172.
Mathematical Reviews (MathSciNet): MR417172
Digital Object Identifier: doi:10.1016/0001-8708(76)90073-6
V. Lakshmibai, K. N. Raghavan, P. Sankaran, and P. Shukla, Standard monomial bases, moduli spaces of vector bundles, and invariant theory, Transform. Groups 11 (2006), 673--704.
Mathematical Reviews (MathSciNet): MR2278144
Digital Object Identifier: doi:10.1007/s00031-005-1123-4
V. Lakshmibai and C. S. Seshadri, Geometry of $G/P$--II. The work of De Concini and Procesi and the basic conjectures, Proc. Indian Acad. Sci. Sect. A 87 (1978), 1--54.
Mathematical Reviews (MathSciNet): MR490244
Digital Object Identifier: doi:10.1007/BF02854528
V. Lakshmibai and P. Shukla, Standard monomial bases and geometric consequences for certain rings of invariants, Proc. Indian Acad. Sci. Math. Sci. 116 (2006), 9--36.
Mathematical Reviews (MathSciNet): MR2210302
Digital Object Identifier: doi:10.1007/BF02829736
V. Mehta and T. R. Ramadas, Moduli of vector bundles, Frobenius splitting, and invariant theory, Ann. of Math. (2) 144 (1996), 269--313.
Mathematical Reviews (MathSciNet): MR1418900
Digital Object Identifier: doi:10.2307/2118593
V. Mehta and A. Ramanathan, Frobenius splitting and cohomology vanishing for Schubert varieties, Ann. of Math. (2) 122 (1985), 27--40.
Mathematical Reviews (MathSciNet): MR799251
Digital Object Identifier: doi:10.2307/1971368
D. Mumford, The red book of varieties and schemes, Lecture Notes in Math., 1358, Springer-Verlag, Berlin, 1988.
Mathematical Reviews (MathSciNet): MR971985
Zentralblatt MATH: 0658.14001
K. E. Smith, Vanishing, singularities and effective bounds via prime characteristic local algebra, Algebraic geometry (Santa Cruz, 1995,) Proc. Sympos. Pure Math., 62, pp. 289--325, Amer. Math. Soc., Providence, RI, 1997.
Mathematical Reviews (MathSciNet): MR1492526
Zentralblatt MATH: 0913.13004
------, Globally $F$-regular varieties: Applications to vanishing theorems for quotients of Fano varieties, Michigan Math. J. 48 (2000), 553--572.
Mathematical Reviews (MathSciNet): MR1786505
Digital Object Identifier: doi:10.1307/mmj/1030132733
Project Euclid: euclid.mmj/1030132733

2009 © The University of Michigan