Multiplication in the cohomology of Grassmannians via Grobner bases

JOURNAL OF ALGEBRA

卷:438

Article

Petrovic, Zoran Z.¹  Prvulovic, Branislav I.¹  Radovanovic, Marko¹ 

[1] Univ Belgrade, Fac Math, Belgrade, Serbia

关键词: Cohomology of Grassmannians;    Grobner bases;    Kostka numbers;    Chem classes;    Stiefel - Whitney classes;    Schubert classes;    Pieri's formula;    Immersions;   

DOI  :  10.1016/j.jalgebra.2015.04.031

来源: Elsevier

【 摘 要 】

In order to gain better understanding of the multiplication in the integral cohomology of the complex Grossmann manifold G(k,n) (C) (in the Borel picture) a minimal strong Grobner basis for the ideal I-k,I-n determining this cohomology is obtained. These results are applied to obtain recurrence relations among Kostka numbers which completely determine these numbers. Corresponding results for real Grossmann manifolds are also presented. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free