Derived categories of small toric Calabi-Yau 3-folds and counting invariants
By K. Nagao. 2008
69 citations recorded by the source corpus.
We first construct a derived equivalence between a small crepant resolution of an affine toric Calabi-Yau 3-fold and a certain quiver with a superpotential. Under this derived equivalence we establish a wall-crossing formula for the generating function of the counting invariants of perverse coherent systems. As an application we provide certain equations on Donaldson-Thomas, Pandeharipande-Thomas and Szendroi's invariants. Finally, we show that moduli spaces associated with a quiver given by successive mutations are realized as the moduli spaces associated the original quiver by changing the stability conditions.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/9cd4df68517a3290b9a2a2c1ebc007651cb9a478
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In Discrete Mathematics and Combinatorics
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Citations in the corpus
- Curve counting theories via stable objects Ⅱ : DT/ncDT flop formula (2009, background): “,AY ), which generalizes Szendro˝i’s non-commutative DT (ncDT for short) invariant for a local (−1,−1)-curve example. It is introduced in [28] and some other local examples are studied in [35], [24], [25]. Our invariant is interpreted as a globalization of the local ncDT-invariant. We consider the g”
- Stability structures, motivic Donaldson-Thomas invariants and cluster transformations (2008, background): “tions from [66] give the following formulas for the invariants Ω(γ): Ω(ncl(Opt)) = −2,n6= 0 ; Ω(ncl(Opt)±cl(OC)) = 1,n∈Z . In all other cases Ω(γ) = 0. For recent generalization of [66] see [49],[50],[51]. 108 7 Quasi-classical limit and integrality conjecture 7.1 Quasi-classical limit, numerical DT”
- Hilbert schemes and stable pairs: GIT and derived category wall crossings (2009, unknown): “A quicker and apparently simpler proof was shown to us by Tom Bridgeland [4], but using the full force of Kontsevich and Soibelman’s theory [13] (which toric Calabi-Yau 3-folds using all of Joyce’s theory, and one using Kontsevich-Soibelman [18].”
- A theory of generalized Donaldson–Thomas invariants (2008, background): “Nagao [83] generalizes this to other toric Calabi–Yau 3-folds.”