Schubert varieties, toric varieties and ladder determinantal varieties
Annales de l'Institut Fourier, Volume 47 (1997) no. 4, pp. 1013-1064.

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.

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 SL(n)/B, Proc. Ind. Acad. Sci., 100 (1990), 45-52] sur les composantes du lieu singulier de certaines variétés de Schubert dans la variété des drapeaux.

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     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},
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     year = {1997},
     doi = {10.5802/aif.1590},
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     url = {http://www.numdam.org/articles/10.5802/aif.1590/}
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Gonciulea, Nicolae; Lakshmibai, Venkatramani. Schubert varieties, toric varieties and ladder determinantal varieties. Annales de l'Institut Fourier, Volume 47 (1997) no. 4, pp. 1013-1064. doi : 10.5802/aif.1590. http://www.numdam.org/articles/10.5802/aif.1590/

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