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• W2100034812 abstract "HTML view is not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button. Let $X$ be a minuscule Schubert variety. In this paper, we associate a quiver with $X$ and use the combinatorics of this quiver to describe all relative minimal models $widehat{pi}:{widehat{X}}to X$. We prove that all the morphisms $widehat{pi}$ are small and give a combinatorial criterion for $widehat{X}$ to be smooth and thus a small resolution of $X$. We describe in this way all small resolutions of $X$. As another application of this description of relative minimal models, we obtain the following more intrinsic statement of the main result of Perrin, J. Algebra 294 (2005), 431–462. Let $alphain A_1(X)$ be an effective 1-cycle class. Then the irreducible components of the scheme Hom$_{alpha}(p^1,X)$ of morphisms from $mathbb{P}^1$ to $X$ and of class $alpha$ are indexed by the set: ${mathfrak{ne}}(alpha)={betain A_1(widehat{X}) mid beta$ is effective and $widehat{pi}_*beta=alpha}$ which is independent of the choice of a relative minimal model $widehat{X}$ of $X$." @default.
• W2100034812 created "2016-06-24" @default.
• W2100034812 creator A5071054174 @default.
• W2100034812 date "2007-09-01" @default.
• W2100034812 modified "2023-09-27" @default.
• W2100034812 title "Small resolutions of minuscule Schubert varieties" @default.
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• W2100034812 doi "https://doi.org/10.1112/s0010437x07002734" @default.
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