A GIT interpretation of the Harder-Narasimhan filtration

作者：Gomez Tomas L^*; Sols Ignacio; Zamora Alfonso

来源：Revista Matematica Complutense, 2015, 28(1): 169-190.

DOI：10.1007/s13163-014-0149-3

• Vector bundles
• Moduli space
• Stability
• Geometric invariant theory

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.

• 出版日期2015-1