Singularites generiques et quasi-resolutions des varietes de Schubert pour le groupe lineaire
Abstract
We determine explicitly the irreducible components of the singular locus of any Schubert variety for GLn(K), K being an algebraically closed field of arbitrary characteristic. We also describe the generic singularities along these components. The case of covexillary Schubert varieties was solved in an earlier work of the author [Ann. Inst. Fourier vol. 51 fasc. 2 (2001), 375-393]. Here, we first exhibit some irreducible components of the singular locus of Xw, by describing the generic singularity along each of them. Let Sw be the union of these components. As mentioned above, the equality Sw = Sing Xw is known for covexillary varieties, and we base our proof of the general case on this result. More precisely, we study the exceptional locus of certain quasi-resolutions of a non-covexillary Schubert variety Xw, and we relate the intersection of these loci to Sw. Then, by induction on the dimension, we can establish the equality.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.