Stability Manifold of P^1
By So Okada. 2004
77 citations recorded by the source corpus.
T. Bridgeland defined the notion of a stability manifold for a triangulated category, motivated by Douglas's work on \Pi-stability for D-branes. We show that the stability manifold of the bounded derived category of the coherent sheaves on P^1 is C^2. This is the first complete picture of a stability manifold for a non-Calabi-Yau manifold.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/c8825216635445c72f8311ecbf18d41b7016bdae
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Geometry and Topology
- Emanuele Macrì
- P. Stellari
- Arend Bayer
- D. Huybrechts
- Yukinobu Toda
- Chunyi Li
- Sukhendu Mehrotra
- Benjamin Schmidt
In Mathematical Physics
- Emanuele Macrì
- Arend Bayer
- P. Stellari
- D. Huybrechts
- Yukinobu Toda
- Sukhendu Mehrotra
- Chunyi Li
- J. Woolf
Citations in the corpus
- Stability conditions for generic K3 categories (2006, background): “A complete description of Stab(X) for a complex projective (or compact) manifold X has only been achieved when X is a curve [Bri02, Mac04, Oka06a].”
- 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].”
- Stability conditions and crepant small resolutions (2005, methodology): “After he wrote the paper [5], some examples have been computed in [7], [8], [10], [29], [ 27 ], [26], [18], [2].”
- Stability conditions, torsion theories and tilting (2009, background): “This example is sufficiently simple to allow explicit computation and yet complicated enough to exhibit all the interesting features of the results.”
- Inducing stability conditions (2007, background): “O := {OP1, OP1(1)} and �O(P 1 ) is equal to the full stability manifold Stab(P 1 ) ([32, 37 ]).”
- Polynomial Bridgeland stability conditions and the large volume limit (2007, methodology): “• For a smooth curve C, stability conditions have been constructed in [Bri07], and Stab(C) has been described by [Mac07, Oka06 ]; in [BK06] the case of singular curves of genus one was considered.”