Another strongly exceptional collection of coherent sheaves on a Grassmannian

JOURNAL OF ALGEBRA

卷:473

Article

Masaharu, Kaneda¹ 

[1] Osaka City Univ, Dept Math, Osaka 5588585, Japan

关键词: Exceptional collection;    Grassmannian;    Frobenius direct image;   

DOI  :  10.1016/j.jalgebra.2016.10.043

来源: Elsevier

【 摘 要 】

On the Grassmannian of 2-dimensional subspaces in a finite dimensional linear space we construct a Karoubian complete strongly exceptional PO set of coherent sheaves, parametrized by the cosets of the Weyl group of the general linear group of the linear space modulo the Weyl group of the parabolic subgroup stabilizing the subspace, from subquotients of the Frobenius direct image of the structure sheaf of the Grassmannian defined over a field of large positive characteristic. Our collection diverges from the one discovered by Kapranov. We also show in the general setting over any field of positive characteristic that the sheaf corresponding to the longest element of the cosets is a direct summand of the Frobenius direct image of the structure sheaf of the homogeneous space. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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