Tomas L. Gomez, Ignacio Sols, Alfonso Zamora
Published 2011-12-08, updated 2014-04-02Version 4
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.
Comments: 19 pages; Comments of the referees and references added. The construction for holomorphic pairs (Sections 6 and 7 from previous version) will appear in a further publication. To appear in Rev. Mat Complutense
On the Harder-Narasimhan filtration for finite dimensional representations of quivers
Harder-Narasimhan filtration for rank 2 tensors and stable coverings
GIT characterizations of Harder-Narasimhan filtrations
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