Bioriented flags and resolutions of Schubert varieties

被引：0

作者：

Cibotaru, Daniel ^{[1
]}

机构：

[1] Univ Fed Ceara, Dept Matemat, BR-60455760 Fortaleza, Ceara, Brazil

来源：

MATHEMATISCHE NACHRICHTEN | 2020年 / 293卷 / 03期

关键词：

flag; Grassmannian; resolution; Schubert; variety; SINGULARITIES; POLYNOMIALS; MORSE;

D O I：

10.1002/mana.201800440

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We use incidence relations running in two directions in order to construct a Kempf-Laksov type resolution for any Schubert variety of the complete flag manifold but also an embedded resolution for any Schubert variety in the Grassmannian. These constructions are alternatives to the celebrated Bott-Samelson resolutions. The second process led to the introduction of W-flag varieties, algebro-geometric objects that interpolate between the standard flag manifolds and products of Grassmannians, but which are singular in general. The surprising simple desingularization of a particular such type of variety produces an embedded resolution of the Schubert variety within the Grassmannian.

引用

页码：449 / 474

页数：26

共 40 条

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