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arXiv · 1112.1886

A GIT interpretration of the Harder-Narasimhan filtration

Tomas L. Gomez·Ignacio Sols·Alfonso Zamora
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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.

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Tomas L. Gomez, Ignacio Sols, Alfonso Zamora. 2014-04-02. A GIT interpretration of the Harder-Narasimhan filtration. https://doi.org/10.1007/s13163-014-0149-3

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