References
H. H. Andersen,Schubert varieties and Demazure’s character formula, Aarhus Preprint Series No. 44, June 1984.
H. H. Andersen, Schubert varieties and Demazure’s character formula,Invent. Math.,79 (1985), 611–618.
M. Demazure, Désingularisations de variétés de Schubert généralisées,Ann. Sci. E.N.S.,7 (1974), 53–88.
R. Hartshorne,Algebraic Geometry, Graduate Texts in Math., Springer-Verlag, 1977.
W. V. D. Hodge andD. Pedoe,Methods of algebraic geometry, Vol. II, Cambridge Univ. Press, 1952.
G. Kempf, Linear Systems on homogeneous spaces,Ann. of Math.,103 (1976), 557–591.
G. Kempf, The Grothendieck-Cousin complex of an induced representation,Adv. in Math.,29 (1978), 310–396.
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.
Lakshmibai andC. S. Seshadri, Geometry of G/P-V,J. of Algebra,100 (1986), 462–557.
Lakshmibai andC. S. Seshadri, Singular locus of a Schubert variety,Bull. A.M.S.,11 (1984), 363–366.
G. Lancaster andJ. Towber, Representation functors and flag algebras for the classical groups I,J. of Algebra,59 (1979), 16–38.
V. B. Mehta andA. Ramanathan, Frobenius splitting and cohomology vanishing for Schubert varieties,Ann. of Math.,122 (1985), 27–40.
D. Mumford,Abelian Varieties, Bombay, Oxford Univ. Press, 1974.
D. Mumford, Varieties defined by quadratic equations, inQuestions on algebraic varieties, Rome, C.I.M.E., 1970, 29–100.
S. Ramanan andA. Ramanathan, Projective normality of flag varieties and Schubert varieties,Invent. Math.,79 (1985), 217–224.
A. Ramanathan, Schubert varieties are arithmetically Cohen-Macaulay,Invent. Math.,80 (1985), 283–294.
C. S. Seshadri, Standard monomial theory and the work of Demazure, inAlgebraic varieties and analytic varieties, Tokyo, 1983, 355–384.
C. S. Seshadri,Normality of Schubert varieties (Preliminary version of [19] below), Manuscript, April 1984.
C. S. Seshadri, Line bundles on Schubert varieties, To appear in theProceedings of the Bombay colloquium on Vector Bundles on Algebraic varieties, 1984.
C. Chevalley,The algebraic theory of spinors, New York, Columbia University Press, 1954.
W. Haboush, Reductive groups are geometrically reductive,Ann. of Math. 102 (1975), 67–84.
Author information
Authors and Affiliations
About this article
Cite this article
Ramanathan, A. Equations defining schubert varieties and frobenius splitting of diagonals. Publications Mathématiques de L’Institut des Hautes Scientifiques 65, 61–90 (1987). https://doi.org/10.1007/BF02698935
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02698935