Equations defining Schubert varieties and Frobenius splittings of diagonals

A. Ramanathan

Publications Mathématiques de l'IHÉS (1987)

  • Volume: 65, page 61-90
  • ISSN: 0073-8301

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Ramanathan, A.. "Equations defining Schubert varieties and Frobenius splittings of diagonals." Publications Mathématiques de l'IHÉS 65 (1987): 61-90. <http://eudml.org/doc/104022>.

@article{Ramanathan1987,
author = {Ramanathan, A.},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {compatibly Frobenius split subvariety; lifting to characteristic zero; generalized Schubert variety; standard monomials; generated by quadrics; characteristic p; higher syzygies},
language = {eng},
pages = {61-90},
publisher = {Institut des Hautes Études Scientifiques},
title = {Equations defining Schubert varieties and Frobenius splittings of diagonals},
url = {http://eudml.org/doc/104022},
volume = {65},
year = {1987},
}

TY - JOUR
AU - Ramanathan, A.
TI - Equations defining Schubert varieties and Frobenius splittings of diagonals
JO - Publications Mathématiques de l'IHÉS
PY - 1987
PB - Institut des Hautes Études Scientifiques
VL - 65
SP - 61
EP - 90
LA - eng
KW - compatibly Frobenius split subvariety; lifting to characteristic zero; generalized Schubert variety; standard monomials; generated by quadrics; characteristic p; higher syzygies
UR - http://eudml.org/doc/104022
ER -

References

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  1. [1] H. H. ANDERSEN, Schubert varieties and Demazure's character formula, Aarhus Preprint Series No. 44, June 1984. Zbl0591.14036
  2. [2] H. H. ANDERSEN, Schubert varieties and Demazure's character formula, Invent. Math., 79 (1985), 611-618. Zbl0591.14036MR86h:14042
  3. [3] M. DEMAZURE, Désingularisations de variétés de Schubert généralisées, Ann. Sci. E.N.S., 7 (1974), 53-88. Zbl0312.14009MR50 #7174
  4. [4] R. HARTSHORNE, Algebraic Geometry, Graduate Texts in Math., Springer-Verlag, 1977. Zbl0367.14001MR57 #3116
  5. [5] W. V. D. HODGE and D. PEDOE, Methods of algebraic geometry, Vol. II, Cambridge Univ. Press, 1952. Zbl0048.14502
  6. [6] G. KEMPF, Linear Systems on homogeneous spaces, Ann. of Math., 103 (1976), 557-591. Zbl0327.14016MR53 #13229
  7. [7] G. KEMPF, The Grothendieck-Cousin complex of an induced representation, Adv. in Math., 29 (1978), 310-396. Zbl0393.20027MR80g:14042
  8. [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. Zbl0336.14001MR55 #2946
  9. [9] LAKSHMIBAI and C. S. SESHADRI, Geometry of G/P-V, J. of Algebra, 100 (1986), 462-557. Zbl0618.14026MR87k:14059
  10. [10] LAKSHMIBAI and C. S. SESHADRI, Singular locus of a Schubert variety, Bull. A.M.S., 11 (1984), 363-366. Zbl0549.14016MR85j:14095
  11. [11] G. LANCASTER and J. TOWBER, Representation functors and flag algebras for the classical groups I, J. of Algebra, 59 (1979), 16-38. Zbl0441.14013MR80i:14020
  12. [12] V. B. MEHTA and A. RAMANATHAN, Frobenius splitting and cohomology vanishing for Schubert varieties, Ann. of Math., 122 (1985), 27-40. Zbl0601.14043MR86k:14038
  13. [13] D. MUMFORD, Abelian Varieties, Bombay, Oxford Univ. Press, 1974. 
  14. [14] D. MUMFORD, Varieties defined by quadratic equations, in Questions on algebraic varieties, Rome, C.I.M.E., 1970, 29-100. Zbl0198.25801MR44 #209
  15. [15] S. RAMANAN and A. RAMANATHAN, Projective normality of flag varieties and Schubert varieties, Invent. Math., 79 (1985), 217-224. Zbl0553.14023MR86j:14051
  16. [16] A. RAMANATHAN, Schubert varieties are arithmetically Cohen-Macaulay, Invent. Math., 80 (1985), 283-294. Zbl0541.14039MR87d:14044
  17. [17] C. S. SESHADRI, Standard monomial theory and the work of Demazure, in Algebraic varieties and analytic varieties, Tokyo, 1983, 355-384. Zbl0569.14024MR85d:14067
  18. [18] C. S. SESHADRI, Normality of Schubert varieties (Preliminary version of [19] below), Manuscript, April 1984. 
  19. [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. Zbl0688.14047
  20. [20] C. CHEVALLEY, The algebraic theory of spinors, New York, Columbia University Press, 1954. Zbl0057.25901MR15,678d
  21. [21] W. HABOUSH, Reductive groups are geometrically reductive, Ann. of Math. 102 (1975), 67-84. Zbl0316.14016MR52 #3179

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