Equations defining Schubert varieties and Frobenius splittings of diagonals
Ramanathan, A.
Publications Mathématiques de l'IHÉS, Tome 66 (1987), p. 61-90 / Harvested from Numdam
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@article{PMIHES_1987__65__61_0,
     author = {Ramanathan, A.},
     title = {Equations defining Schubert varieties and Frobenius splittings of diagonals},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     volume = {66},
     year = {1987},
     pages = {61-90},
     mrnumber = {88k:14032},
     zbl = {0634.14035},
     language = {en},
     url = {http://dml.mathdoc.fr/item/PMIHES_1987__65__61_0}
}

Ramanathan, A. Equations defining Schubert varieties and Frobenius splittings of diagonals. Publications Mathématiques de l'IHÉS, Tome 66 (1987) pp. 61-90. http://gdmltest.u-ga.fr/item/PMIHES_1987__65__61_0/

[1] H. H. Andersen, Schubert varieties and Demazure's character formula, Aarhus Preprint Series No. 44, June 1984. | Zbl 0591.14036

[2] H. H. Andersen, Schubert varieties and Demazure's character formula, Invent. Math., 79 (1985), 611-618. | MR 86h:14042 | Zbl 0591.14036

[3] M. Demazure, Désingularisations de variétés de Schubert généralisées, Ann. Sci. E.N.S., 7 (1974), 53-88. | Numdam | MR 50 #7174 | Zbl 0312.14009

[4] R. Hartshorne, Algebraic Geometry, Graduate Texts in Math., Springer-Verlag, 1977. | MR 57 #3116 | Zbl 0367.14001

[5] W. V. D. Hodge and D. Pedoe, Methods of algebraic geometry, Vol. II, Cambridge Univ. Press, 1952.

[6] G. Kempf, Linear Systems on homogeneous spaces, Ann. of Math., 103 (1976), 557-591. | MR 53 #13229 | Zbl 0327.14016

[7] G. Kempf, The Grothendieck-Cousin complex of an induced representation, Adv. in Math., 29 (1978), 310-396. | MR 80g:14042 | Zbl 0393.20027

[8] S. L. Kleiman, Rigorous foundation for Schubert's enumerative calculus, in Mathematical developments arising from Hilbert problems, A.M.S. Proc. of Symposia in Pure Math., Vol. XXVIII (1976), 445-482. | MR 55 #2946 | Zbl 0336.14001

[9] Lakshmibai and C. S. Seshadri, Geometry of G/P-V, J. of Algebra, 100 (1986), 462-557. | MR 87k:14059 | Zbl 0618.14026

[10] Lakshmibai and C. S. Seshadri, Singular locus of a Schubert variety, Bull. A.M.S., 11 (1984), 363-366. | MR 85j:14095 | Zbl 0549.14016

[11] G. Lancaster and J. Towber, Representation functors and flag algebras for the classical groups I, J. of Algebra, 59 (1979), 16-38. | MR 80i:14020 | Zbl 0441.14013

[12] V. B. Mehta and A. Ramanathan, Frobenius splitting and cohomology vanishing for Schubert varieties, Ann. of Math., 122 (1985), 27-40. | MR 86k:14038 | Zbl 0601.14043

[13] D. Mumford, Abelian Varieties, Bombay, Oxford Univ. Press, 1974.

[14] D. Mumford, Varieties defined by quadratic equations, in Questions on algebraic varieties, Rome, C.I.M.E., 1970, 29-100. | MR 44 #209 | Zbl 0198.25801

[15] S. Ramanan and A. Ramanathan, Projective normality of flag varieties and Schubert varieties, Invent. Math., 79 (1985), 217-224. | MR 86j:14051 | Zbl 0553.14023

[16] A. Ramanathan, Schubert varieties are arithmetically Cohen-Macaulay, Invent. Math., 80 (1985), 283-294. | MR 87d:14044 | Zbl 0541.14039

[17] C. S. Seshadri, Standard monomial theory and the work of Demazure, in Algebraic varieties and analytic varieties, Tokyo, 1983, 355-384. | MR 85d:14067 | Zbl 0569.14024

[18] C. S. Seshadri, Normality of Schubert varieties (Preliminary version of [19] below), Manuscript, April 1984.

[19] C. S. Seshadri, Line bundles on Schubert varieties, To appear in the Proceedings of the Bombay colloquium on Vector Bundles on Algebraic varieties, 1984. | Zbl 0688.14047

[20] C. Chevalley, The algebraic theory of spinors, New York, Columbia University Press, 1954. | MR 15,678d | Zbl 0057.25901

[21] W. Haboush, Reductive groups are geometrically reductive, Ann. of Math. 102 (1975), 67-84. | MR 52 #3179 | Zbl 0316.14016