Stability Conditions for Slodowy Slices and Real Variations of Stability
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Stability conditions for slodowy.pdf
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Author(s)
Mirkovic, Ivan
Anno, Irina
Bezrukavnikov, Roman
Date Issued
April 2015
Journal
Moscow Mathematical Journal
Publisher
Independent University of Moscow
Citation
Anno, Rino, Roman Bezrukavnikov, and Ivan Mirković. "Stability Conditions for Slodowy Slices and Real Variations of Stability." Moscow Mathematical Journal 15.2 (2015) 187–203.
Version
Author's final manuscript
Abstract
The paper provides new examples of an explicit submanifold in
Bridgeland stabilities space of a local Calabi-Yau. More precisely, let X be the standard resolution of a transversal slice to an adjoint nilpotent orbit of a simple Lie algebra over C. An action of the affine braid group on the derived category D[superscript b] (Coh(X)) and a collection of t-structures on this category permuted by the action have been constructed in [BR] and [BM] respectively. In this note we show that the t-structures come from points in a certain connected submanifold in the space of Bridgeland
stability conditions. The submanifold is a covering of a submanifold in the
dual space to the Grothendieck group, and the affine braid group acts by deck transformations. We also propose a new variant of definition of stabilities on a triangulated category, which we call a ”real variation of stability conditions” and discuss its relation to Bridgeland’s definition. The main theorem provides an illustration of such a relation. We state a conjecture by the second author and A. Okounkov on examples of this structure arising from symplectic resolutions of singularities and its relation to equivariant quantum cohomology. We verify this conjecture in our examples.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
http://www.mathjournals.org/mmj/2015-015-002/2015-015-002-002.html
