Stability conditions and crepant small resolutions
By Yukinobu Toda. 2005
69 citations recorded by the source corpus.
In this paper, we describe the spaces of stability conditions on the triangulated categories associated to three dimensional crepant small resolutions. The resulting spaces have chamber structures such that each chamber corresponds to a birational model together with a special Fourier-Mukai transform. We observe that these spaces are covering spaces over certain open subsets of finite dimensional vector spaces and determine their deck transformations.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/887431b6c37001676ff2aa0b522265d9260ab4a8
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In Geometry and Topology
- Yukinobu Toda
- Arend Bayer
- M. Wemyss
- Balázs Szendrői
- Emanuele Macrì
- Chunyi Li
- P. Stellari
- D. Huybrechts
In Mathematical Physics
Citations in the corpus
- Moduli stacks and invariants of semistable objects on K3 surfaces (2007, background): “Such invariants are expected to produce automorphic functions on the space of stability conditions in the sense of T. Bridgeland [7].”
- Non-commutative Donaldson-Thomas theory and the conifold (2007, background): “ng C. By [6], Stab(X/Z) is a one-dimensional complex manifold. Let finally DAut(X/Z) be the subgroup of the derived autoequivalence group of D(X/Z) which preserves this component. Then it is proved in [7, 28] that Stab(X/Z)/DAut(X/Z) ∼= P1 \ {0,1,∞}. In physics language, this is the full complexified ”
- Flops and clusters in the homological minimal model programme (2014, background): “It also means, for example, that any naive extension of [46] or [7,14] is not possible, since root systems andWeyl groups do not necessarily appear.”
- Polynomial Bridgeland stability conditions and the large volume limit (2007, background): “Some of the stability conditions constructed in this article have also been constructed independently by Yukinobu Toda in [Tod08a], namely the stabili y conditions at the large volume limit of Calabi-Yau threefolds.”
- The space of stability conditions on the local projective plane (2009, unknown): “Other local Calabi-Yau threefold cases were studied in [ Tod08b , Tod09], and, as already mentioned, an open subset of Staby(D0) has been described in [Bri06].”