Nous construisons des variétés toriques normales (associées à des treillis distributifs finis) qui sont des grassmanniennes dégénérées. Nous déterminons aussi les lieux singuliers de ces variétés toriques, dans le cas où elles sont des variétés déterminantielles échelonnées (ladder determinantal varieties). Nous prouvons une version raffinée de la conjecture de Laksmibai & Sandhya [Criterion for smoothness of Schubert varieties in , Proc. Ind. Acad. Sci., 100 (1990), 45-52] sur les composantes du lieu singulier de certaines variétés de Schubert dans la variété des drapeaux.
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 , Proc. Ind. Acad. Sci., 100 (1990), 45-52] on the components of the singular locus, for certain Schubert varieties in the flag variety.
@article{AIF_1997__47_4_1013_0,
author = {Gonciulea, Nicolae and Lakshmibai, Venkatramani},
title = {Schubert varieties, toric varieties and ladder determinantal varieties},
journal = {Annales de l'Institut Fourier},
pages = {1013--1064},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {47},
number = {4},
year = {1997},
doi = {10.5802/aif.1590},
zbl = {0878.14033},
mrnumber = {99a:14078},
language = {en},
url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1590/}
}
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 SP - 1013 EP - 1064 VL - 47 IS - 4 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1590/ DO - 10.5802/aif.1590 LA - en ID - AIF_1997__47_4_1013_0 ER -
%0 Journal Article %A Gonciulea, Nicolae %A Lakshmibai, Venkatramani %T Schubert varieties, toric varieties and ladder determinantal varieties %J Annales de l'Institut Fourier %D 1997 %P 1013-1064 %V 47 %N 4 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.1590/ %R 10.5802/aif.1590 %G en %F AIF_1997__47_4_1013_0
Gonciulea, Nicolae; Lakshmibai, Venkatramani. Schubert varieties, toric varieties and ladder determinantal varieties. Annales de l'Institut Fourier, Tome 47 (1997) no. 4, pp. 1013-1064. doi : 10.5802/aif.1590. https://aif.centre-mersenne.org/articles/10.5802/aif.1590/
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