The space of stability conditions on the local projective plane
By Arend Bayer, Emanuele Macrì. 2009
132 citations recorded by the source corpus.
We study the space of stability conditions on the total space of the canonical bundle over the projective plane. We explicitly describe a chamber of geometric stability conditions, and show that its translates via autoequivalences cover a whole connected component. We prove that this connected component is simply-connected. We determine the group of autoequivalences preserving this connected component, which turns out to be closely related to 1(3). Finally, we show that there is a submanifold isomorphic to the univer- sal covering of a moduli space of elliptic curves with 1(3)-level struc- ture. The morphism is 1(3)-equivariant, and is given by solutions of Picard-Fuchs equations. This result is motivated by the notion of - stability and by mirror symmetry.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/1de28df0898f72335dde087e3f6ecb54d1cd35e2
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In Geometry and Topology
- Emanuele Macrì
- Benjamin Schmidt
- Chunyi Li
- Xiaolei Zhao
- Arend Bayer
- I. Smith
- Jack Huizenga
- Yukinobu Toda
In Mathematical Physics
- Benjamin Schmidt
- Emanuele Macrì
- Chunyi Li
- Xiaolei Zhao
- Jack Huizenga
- I. Smith
- Yukinobu Toda
- Arend Bayer
Citations in the corpus
- Birational models of moduli spaces of coherent sheaves on the projective plane (2016, background): “In this section, we follow [5; 11] and recall that the space of geometric stability conditions on P(2) is a e GLC.”
- Quadratic differentials as stability conditions (2013, methodology): “Property (b) follows from the identity TwTwSi(Sj) = TwSi ◦TwSj ◦Tw −1 Si , and the fact that TwSi[1] = TwSi.”
- Lectures on Bridgeland Stability (2016, methodology): “ σ-semistable objects is defined analogously as well. The support property was introduced in [KS08]; it is equivalent to Bridgeland’s notion of a full locally-finite stability condition in [Bri08] (see [BM11]). There is an equivalent formulation: There is a symmetric bilinear form Q on ΛR such that (1”
- The Minimal Model Program for the Hilbert Scheme of Points on P^2 and Bridgeland Stability (2012, methodology): “isfy r(E) = d(E) = 0 and the Bogomolov inequality, it is immediate that the triples (As;rt,dt) are pre-stability conditions. The finiteness of Harder-Narasimhan filtrations is proved by Bayer-Macr`ı in [BM]. Fix a triple of numbers defining a Chern character (r,c,d) ❀(r,cL,dL2) on P2 (rand care integer”