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.
"Stratifications of parameter spaces for complexes by cohomology types." J. Math. Soc. Japan 67 (1) 43 - 68, January, 2015. https://doi.org/10.2969/jmsj/06710043