Desingularizations of Schubert varieties in double Grassmannians

Details Desingularizations of Schubert varieties in double Grassmannians Desingularizations of Schubert varieties in double Grassmannians

2006-08-22

arxiv.org/abs/math/0608554v3

Funct. Anal. Appl. 42 (2008), no. 2, 126-134

Mathematics

Algebraic Geometry

12 pages; uses youngtab.sty. Version 2: minor editorial changes, final version published in Funct. Anal. Appl

Scientific paper

Let X be the direct product of two Grassmann varieties of k- and l-planes in a finite-dimensional vector space V, and let B be the isotropy group of a complete flag in V. We consider B-orbits in X, which are an analog to Schubert cells in Grassmannians. We describe this set of orbits combinatorially and construct desingularizations for the closures of these orbits, similar to the Bott--Samelson desingularizations for Schubert varieties.

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