Degeneration of Schubert varieties of S L n / B to toric varieties

Raika Dehy[1]; Rupert W.T. Yu[2]

  • [1] Université de Cergy-Pontoise, Département de Mathématiques, 2 avenue Adolphe Chauvin, 95032 Cergy Cedex (France)
  • [2] Université de Poitiers, Département de Mathématiques, Boulevard Marie et Pierre Curie, Téléport 2, BP 30179, 86962 Futuroscope Chasseneuil Cedex (France)

Annales de l’institut Fourier (2001)

  • Volume: 51, Issue: 6, page 1525-1538
  • ISSN: 0373-0956

Abstract

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Using the polytopes defined in an earlier paper, we show in this paper the existence of degeneration of a large class of Schubert varieties of S L n to toric varieties by extending the method used by Gonciulea and Lakshmibai for a miniscule G / P to Schubert varieties in S L n .

How to cite

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Dehy, Raika, and Yu, Rupert W.T.. "Degeneration of Schubert varieties of $SL_n/B$ to toric varieties." Annales de l’institut Fourier 51.6 (2001): 1525-1538. <http://eudml.org/doc/115957>.

@article{Dehy2001,
abstract = {Using the polytopes defined in an earlier paper, we show in this paper the existence of degeneration of a large class of Schubert varieties of $SL_\{n\}$ to toric varieties by extending the method used by Gonciulea and Lakshmibai for a miniscule $G/P$ to Schubert varieties in $SL_\{n\}$.},
affiliation = {Université de Cergy-Pontoise, Département de Mathématiques, 2 avenue Adolphe Chauvin, 95032 Cergy Cedex (France); Université de Poitiers, Département de Mathématiques, Boulevard Marie et Pierre Curie, Téléport 2, BP 30179, 86962 Futuroscope Chasseneuil Cedex (France)},
author = {Dehy, Raika, Yu, Rupert W.T.},
journal = {Annales de l’institut Fourier},
keywords = {Schubert varieties; toric varieties; flat deformations; distributive lattice; standard monomial basis},
language = {eng},
number = {6},
pages = {1525-1538},
publisher = {Association des Annales de l'Institut Fourier},
title = {Degeneration of Schubert varieties of $SL_n/B$ to toric varieties},
url = {http://eudml.org/doc/115957},
volume = {51},
year = {2001},
}

TY - JOUR
AU - Dehy, Raika
AU - Yu, Rupert W.T.
TI - Degeneration of Schubert varieties of $SL_n/B$ to toric varieties
JO - Annales de l’institut Fourier
PY - 2001
PB - Association des Annales de l'Institut Fourier
VL - 51
IS - 6
SP - 1525
EP - 1538
AB - Using the polytopes defined in an earlier paper, we show in this paper the existence of degeneration of a large class of Schubert varieties of $SL_{n}$ to toric varieties by extending the method used by Gonciulea and Lakshmibai for a miniscule $G/P$ to Schubert varieties in $SL_{n}$.
LA - eng
KW - Schubert varieties; toric varieties; flat deformations; distributive lattice; standard monomial basis
UR - http://eudml.org/doc/115957
ER -

References

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  1. C. de Concini, D. Eisenbud, C. Procesi, Hodge algebras, Astérisque 91 (1982) Zbl0509.13026MR680936
  2. R. Dehy, Polytopes associated to Demazure modules of Symmetrizable Kac-Moody algebras of rank two, Journal of Algebra 228 (2000), 60-90 Zbl0973.17033MR1760956
  3. R. Dehy, R.W.T. Yu, Polytopes associated to certain Demazure modules of 𝔰 l ( n ) , Journal of Algebraic Combinatorics 10 (1999), 149-172 Zbl0966.17004MR1719132
  4. D. Eisenbud, B. Sturmfels, Binomial ideals, Duke Math. J. 84 (1996), 1-45 Zbl0873.13021MR1394747
  5. N. Gonciulea, V. Lakshmibai, Degenerations of flag and Schubert varieties to toric varieties, Transformation Groups 2 (1996), 215-249 Zbl0909.14028MR1417711
  6. T. Hibi, Distributive lattices, affine semigroup rings, and algebras with straightening laws, Commutative algebra and combinatorics 11 (1987), 93-109 Zbl0654.13015
  7. C. Huneke, V. Lakshmibai, Degeneracy of Schubert varieties., Kazhdan-Lusztig theory and related topics (Chicago, IL, 1989) 139 (1992), 181-235, Amer. Math. Soc., Providence, RI Zbl0806.14036
  8. G. Kempf, A. Ramanthan, Multicones over Schubert Varieties, Invent. Math. 87 (1987), 353-363 Zbl0615.14028MR870733
  9. V. Lakshmibai, C. Musili, C. S. Seshadri, Geometry of G / P . IV. Standard monomial theory for classical types, Proc. Indian Acad. Sci., Sect. A Math. Sci 88 (1979), 279-362 Zbl0447.14013MR553746
  10. V. Lakshmibai, C. S. Seshadri, Geometry of G / P . V, J. Algebra 100 (1986), 462-557 Zbl0618.14026MR840589
  11. B. Teissier, Variétés toriques et polytopes, Séminaire Bourbaki 901, exposé 565 (1981), 71-84, Springer-Verlag, New York Zbl0494.52010

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