Stratifications of parameter spaces for complexes by cohomology types

Details Stratifications of parameter spaces for complexes by cohomology types Stratifications of parameter spaces for complexes by cohomology types

2012-02-16

arxiv.org/abs/1202.3630v1

Mathematics

Algebraic Geometry

23 pages

Scientific paper

We study a collection of stability conditions (in the sense of Schmitt) for complexes of sheaves over a smooth complex projective variety indexed by a positive rational parameter. We show that the Harder-Narasimhan filtration of a complex for small values of this parameter encodes the Harder-Narasimhan filtrations of the cohomology sheaves of this complex. Finally we relate a stratification into locally closed subschemes of a parameter space for complexes associated to these stability parameters with the stratification by Harder-Narasimhan types.

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