✦ LIBER ✦

Singular Loci of Ladder Determinantal Varieties and Schubert Varieties: Volume 229, Number 2 (2000), pages 463–497

✍ Scribed by N. Gonciulea; V. Lakshmibai

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 291 KB
Volume: 232
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.2000.8558

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✦ Synopsis

We relate certain ladder determinantal varieties (associated to one-sided ladders) to certain Schubert varieties in SL n /Q, for a suitable n and a suitable parabolic subgroup Q, and we determine the singular loci of these varieties. We state a conjecture on the irreducible components of the singular locus of a Schubert variety in the flag variety, which is a refinement of the conjecture of Lakshmibai and Sandhya (Proc. Indian Acad. Sci. Math. Sci. 100 (1990), 45-52). We prove the conjecture for a certain class of Schubert varieties.