2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/107412In 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.64 pages, in english. According to a remark of B. Totaro, we add a reference to J. Wisniewski which was essential in the proof of the theorem: any small resolution is a relative minimal model. We reattribute this result to B. Totaro and J. WisniewskiAlgebraic GeometryRepresentation Theory14M15, 14E30, 05E15text