A GIT interpretration of the Harder-Narasimhan filtration

Details A GIT interpretration of the Harder-Narasimhan filtration A GIT interpretration of the Harder-Narasimhan filtration

2011-12-08

arxiv.org/abs/1112.1886v2

Mathematics

Algebraic Geometry

29 pages; references added and analogous result for holomorphic pairs

Scientific paper

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 coincides with the Harder-Narasimhan filtration. Then we prove the analogous result for holomorphic pairs.

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