Small resolutions of minuscule Schubert varieties

Details Small resolutions of minuscule Schubert varieties Small resolutions of minuscule Schubert varieties

2006-01-06

arxiv.org/abs/math/0601117v2

Mathematics

Algebraic Geometry

64 pages, in english. According to a remark of B. Totaro, we add a reference to J. Wisniewski which was essential in the proof

Scientific paper

In this paper, we describe on the one hand, all relative minimal models Y of a minuscule Schubert variety X using some combinatorics on quivers and we prove that the morphism from Y to X is small (in the sense of intersection cohomology). On the other hand, thanks to a result of B. Totaro, any small resolution Z of a minuscule Schubert variety X has to be a relative minimal model of X. So X admits a small resolution if and only if there exists a smooth relative minimal model Y of X. We give a combinatoric criterion for Y to be smooth describing in this way all small resolutions of X. We also use stringy polynomials and the relative canonical model to give another way to tell when a minuscule Schubert variety admits a small resolution.

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