Schubert varieties, toric varieties and ladder determinantal varieties

Nicolae Gonciulea; Venkatramani Lakshmibai

Annales de l'institut Fourier (1997)

  • Volume: 47, Issue: 4, page 1013-1064
  • ISSN: 0373-0956

Abstract

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We construct certain normal toric varieties (associated to finite distributive lattices) which are degenerations of the Grassmannians. We also determine the singular loci for certain normal toric varieties, namely the ones which are certain ladder determinantal varieties. As a consequence, we prove a refined version of the conjecture of Laksmibai & Sandhya [Criterion for smoothness of Schubert varieties in S L ( n ) / B , Proc. Ind. Acad. Sci., 100 (1990), 45-52] on the components of the singular locus, for certain Schubert varieties in the flag variety.

How to cite

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Gonciulea, Nicolae, and Lakshmibai, Venkatramani. "Schubert varieties, toric varieties and ladder determinantal varieties." Annales de l'institut Fourier 47.4 (1997): 1013-1064. <http://eudml.org/doc/75253>.

@article{Gonciulea1997,
abstract = {We construct certain normal toric varieties (associated to finite distributive lattices) which are degenerations of the Grassmannians. We also determine the singular loci for certain normal toric varieties, namely the ones which are certain ladder determinantal varieties. As a consequence, we prove a refined version of the conjecture of Laksmibai & Sandhya [Criterion for smoothness of Schubert varieties in $SL(n)/B$, Proc. Ind. Acad. Sci., 100 (1990), 45-52] on the components of the singular locus, for certain Schubert varieties in the flag variety.},
author = {Gonciulea, Nicolae, Lakshmibai, Venkatramani},
journal = {Annales de l'institut Fourier},
keywords = {Schubert varieties; toric varieties; ladder determinantal varieties; distributive lattices; singular locus; flag variety},
language = {eng},
number = {4},
pages = {1013-1064},
publisher = {Association des Annales de l'Institut Fourier},
title = {Schubert varieties, toric varieties and ladder determinantal varieties},
url = {http://eudml.org/doc/75253},
volume = {47},
year = {1997},
}

TY - JOUR
AU - Gonciulea, Nicolae
AU - Lakshmibai, Venkatramani
TI - Schubert varieties, toric varieties and ladder determinantal varieties
JO - Annales de l'institut Fourier
PY - 1997
PB - Association des Annales de l'Institut Fourier
VL - 47
IS - 4
SP - 1013
EP - 1064
AB - We construct certain normal toric varieties (associated to finite distributive lattices) which are degenerations of the Grassmannians. We also determine the singular loci for certain normal toric varieties, namely the ones which are certain ladder determinantal varieties. As a consequence, we prove a refined version of the conjecture of Laksmibai & Sandhya [Criterion for smoothness of Schubert varieties in $SL(n)/B$, Proc. Ind. Acad. Sci., 100 (1990), 45-52] on the components of the singular locus, for certain Schubert varieties in the flag variety.
LA - eng
KW - Schubert varieties; toric varieties; ladder determinantal varieties; distributive lattices; singular locus; flag variety
UR - http://eudml.org/doc/75253
ER -

References

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