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SPLITTING CRITERIA FOR VECTOR BUNDLES ON MINUSCULE HOMOGENEOUS VARIETIES

SPLITTING CRITERIA FOR VECTOR BUNDLES ON MINUSCULE HOMOGENEOUS VARIETIES We prove that a vector bundle on a minuscule homogeneous variety splits into a direct sum of line bundles if and only if its restriction to the union of two-dimensional Schubert subvarieties splits. A case-by-case analysis is done. The result largely generalizes Horrocks’ splitting criterion for vector bundles on projective spaces. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Transformation Groups Springer Journals

SPLITTING CRITERIA FOR VECTOR BUNDLES ON MINUSCULE HOMOGENEOUS VARIETIES

Transformation Groups , Volume 22 (3) – Mar 30, 2016

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References (24)

Publisher
Springer Journals
Copyright
Copyright © 2016 by Springer Science+Business Media New York
Subject
Mathematics; Topological Groups, Lie Groups; Algebra
ISSN
1083-4362
eISSN
1531-586X
DOI
10.1007/s00031-016-9371-z
Publisher site
See Article on Publisher Site

Abstract

We prove that a vector bundle on a minuscule homogeneous variety splits into a direct sum of line bundles if and only if its restriction to the union of two-dimensional Schubert subvarieties splits. A case-by-case analysis is done. The result largely generalizes Horrocks’ splitting criterion for vector bundles on projective spaces.

Journal

Transformation GroupsSpringer Journals

Published: Mar 30, 2016

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