Equations defining Schubert varieties and Frobenius splittings of diagonals
Publications Mathématiques de l'IHÉS, Volume 65 (1987), pp. 61-90.
@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},
     pages = {61--90},
     publisher = {Institut des Hautes \'Etudes Scientifiques},
     volume = {65},
     year = {1987},
     mrnumber = {908216},
     zbl = {0634.14035},
     language = {en},
     url = {http://archive.numdam.org/item/PMIHES_1987__65__61_0/}
}
TY  - JOUR
AU  - Ramanathan, A.
TI  - Equations defining Schubert varieties and Frobenius splittings of diagonals
JO  - Publications Mathématiques de l'IHÉS
PY  - 1987
SP  - 61
EP  - 90
VL  - 65
PB  - Institut des Hautes Études Scientifiques
UR  - http://archive.numdam.org/item/PMIHES_1987__65__61_0/
LA  - en
ID  - PMIHES_1987__65__61_0
ER  - 
%0 Journal Article
%A Ramanathan, A.
%T Equations defining Schubert varieties and Frobenius splittings of diagonals
%J Publications Mathématiques de l'IHÉS
%D 1987
%P 61-90
%V 65
%I Institut des Hautes Études Scientifiques
%U http://archive.numdam.org/item/PMIHES_1987__65__61_0/
%G en
%F PMIHES_1987__65__61_0
Ramanathan, A. Equations defining Schubert varieties and Frobenius splittings of diagonals. Publications Mathématiques de l'IHÉS, Volume 65 (1987), pp. 61-90. http://archive.numdam.org/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

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

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

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

[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 | Zbl

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

[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 | Zbl

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

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

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

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

[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 | Zbl

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

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

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

[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

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

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