The arc space of the Grassmannian

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• 作者：Roi Docampo^a ; ^{roi.docampo@icmat.es} ; Antonio Nigro^b ; ^{nigro@impa.br}
• 关键词：primary ; 14E18 ; 14M15 ; secondary ; 14B05
• 刊名：Advances in Mathematics
• 出版年：2017
• 出版时间：14 January 2017
• 年：2017
• 卷：306
• 期：Complete
• 页码：1269-1332
• 全文大小：1332 K
• 卷排序：306

文摘

We study the arc space of the Grassmannian from the point of view of the singularities of Schubert varieties. Our main tool is a decomposition of the arc space of the Grassmannian that resembles the Schubert cell decomposition of the Grassmannian itself. Just as the combinatorics of Schubert cells is controlled by partitions, the combinatorics in the arc space is controlled by plane partitions (sometimes also called 3d partitions). A combination of a geometric analysis of the pieces in the decomposition and a combinatorial analysis of plane partitions leads to invariants of the singularities. As an application we reduce the computation of log canonical thresholds of pairs involving Schubert varieties to an easy linear programming problem. We also study the Nash problem for Schubert varieties, showing that the Nash map is always bijective in this case.