Journal of the Mathematical Society of Japan

Stratifications of parameter spaces for complexes by cohomology types

Victoria HOSKINS

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

First available in Project Euclid: 22 January 2015

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Zentralblatt MATH identifier

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]

geometric invariant theory stratifications complexes of sheaves


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.

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