Cohomology of line bundles on Schubert varieties. I
type: Item
instance of: scholarly article
title: Cohomology of line bundles on Schubert varieties. I
zbMATH Open document ID: 1078.14071
author: K. V. Subrahmanyam
author: V. Balaji
author: Subramaniam Senthamarai Kannan
published in: Transformation Groups
publication date: 2004-12-13T00:00:00Z
review text: The authors investigate the cohomology modules \(H^i(X(w),L_\lambda)\), for \(\lambda\) non-dominant on a Schubert variety \(X (w)\) in the generalized flag variety, especially, the vanishing or non-vanishing of \(H^i(X(\omega), L_\lambda)\). For a generic \(\lambda\), the authors give a criterion for vanishing (resp. non-vanishing) of \(H^{l(w)}(X (w), L_\lambda)\) (resp. \(H^0(X(w), L_\lambda)\)). For a general \(j\), the authors give partial results on the vanishing of \(H^j(X(w), L_\lambda)\).
Mathematics Subject Classification ID: 14M15
Mathematics Subject Classification ID: 20G05
zbMATH DE Number: 2121803
zbMATH Keywords: cohomology
zbMATH Keywords: line bundles
zbMATH Keywords: Schubert varieties
reviewed by: V. Lakshmibai
MaRDI profile type: Publication
full work available at URL: s00031-004-7007-1
OpenAlex ID: W2039653807
DOI: 10.1007/S00031-004-7007-1
description: scientific article; zbMATH DE number 2121803