Journal of the Mathematical Society of Japan

Stratifications of parameter spaces for complexes by cohomology types

Victoria HOSKINS

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Abstract

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.

Article information

Source
J. Math. Soc. Japan, Volume 67, Number 1 (2015), 43-68.

Dates
First available in Project Euclid: 22 January 2015

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1421936545

Digital Object Identifier
doi:10.2969/jmsj/06710043

Mathematical Reviews number (MathSciNet)
MR3304014

Zentralblatt MATH identifier
1349.14153

Subjects
Primary: 14L24: Geometric invariant theory [See also 13A50] 14D20: Algebraic moduli problems, moduli of vector bundles {For analytic moduli problems, see 32G13}
Secondary: 14L30: Group actions on varieties or schemes (quotients) [See also 13A50, 14L24, 14M17] 14F05: Sheaves, derived categories of sheaves and related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20]

Keywords
geometric invariant theory stratifications complexes of sheaves

Citation

HOSKINS, Victoria. Stratifications of parameter spaces for complexes by cohomology types. J. Math. Soc. Japan 67 (2015), no. 1, 43--68. doi:10.2969/jmsj/06710043. https://projecteuclid.org/euclid.jmsj/1421936545


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