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A GIT interpretration of the Harder-Narasimhan filtration

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Gómez, Tomás L. and Sols, Ignacio and Alfonso, Zamora (2015) A GIT interpretration of the Harder-Narasimhan filtration. Revista matemática complutense, 28 (1). pp. 169-190. ISSN 1139-1138

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Official URL: http://link.springer.com/article/10.1007/s13163-014-0149-3


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http://arxiv.org/abs/1112.1886Organisation


Abstract

An unstable torsion free sheaf on a smooth projective variety gives a GIT unstable point in certain Quot scheme. To a GIT unstable point, Kempf associates a "maximally destabilizing" 1-parameter subgroup, and this induces a filtration of the torsion free sheaf. We show that this filtration coincides with the Harder-Narasimhan filtration.


Item Type:Article
Uncontrolled Keywords:Vector bundles; Moduli space; Stability; Geometric invariant theory
Subjects:Sciences > Mathematics
ID Code:29073
Deposited On:06 Mar 2015 08:38
Last Modified:06 Mar 2015 08:38

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