Gromov–Witten theory and Donaldson–Thomas theory, II

By Davesh Maulik, N. Nekrasov, A. Okounkov, R. Pandharipande. Compositio Mathematica, 2004

158 citations recorded by the source corpus.

We discuss the Gromov–Witten/Donaldson–Thomas correspondence for 3-folds in both the absolute and relative cases. Descendents in Gromov–Witten theory are conjectured to be equivalent to Chern characters of the universal sheaf in Donaldson–Thomas theory. Relative constraints in Gromov–Witten theory are conjectured to correspond in Donaldson–Thomas theory to cohomology classes of the Hilbert scheme of points of the relative divisor. Independent of the conjectural framework, we prove degree 0 formulas for the absolute and relative Donaldson–Thomas theories of toric varieties.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9e95fdcf4c4c46e9b2aede09edc793f24654fa5f

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Citations in the corpus

Split states, entropy enigmas, holes and halos (2007, background): “Granted this point, the identifications are interpreted as follows: At large volume, rank 1 D6-D2-D0 bound states are described by ideal sheaves I [80, 33, 34, 32] or their duals I∗.”
The local Donaldson–Thomas theory of curves (2005, methodology): “The evaluations (6) and (7) are Theorem 1 and Corollary 1 of [25] with an appropriate adjustment of signs to match the conventions here.”
Quot schemes of curves and surfaces: virtual classes, integrals, Euler characteristics (2019, methodology): “The parallel study for 3-folds was undertaken in [37, 38] and led to the MacMahon function for Hilbert schemes of points and the GW/DT correspondence for Hilbert schemes of curves.”
Lectures on black holes, topological strings and quantum attractors (2006, unknown): “S-duality implies [72, 73] that the partition function of Donaldson-Thomas invariants is related to the partition function of Gromov-Witten invariants by [74, 75] ∑ qA∈H2(Z),m∈Z nDT (qA, m)e itAq A q = exp [ FGW (t, λ) − χ 2 f(λ) ] (4.”
D-brane Deconstructions in IIB Orientifolds (2008, background): “However they can still be described by sheaves, more precisely they are rank 1 ideal sheaves [122, 123].”
Refined, Motivic, and Quantum (2009, background): “Of course, the quantity w∞(Θ ) must be the Donaldson-Thomas partition function of the conifold, and this relation holds because pyramid partitions of length n→∞ effectively reduce to the topological vertex formalism of [12,13] (see also [27,28]).”
The Superpolynomial for Knot Homologies (2005, methodology): “For example, the genuscounting parameter u in the open Gromov–Witten theory is related to the variable q that we use via the following change of variables (also familiar in the context of the closed Gromov–Witten theory [Maulik et al. 05]): q = eiu.”
Computation of Open Gromov–Witten Invariants for Toric Calabi–Yau 3-Folds by Topological Recursion, a Proof of the BKMP Conjecture (2012, unknown): “11 03 v2 [ m at”
A mathematical theory of the topological vertex (2004, background): “Maulik, Nekrasov, Okounkov, and Pandharipande conjectured a correspondence between the Gromov-Witten and Donaldson-Thomas theories for any non-singular projective threefold [36, 37].”
Brane tilings and their applications (2008, unknown): “Since their generating function coincide with Gromov-Witten invariants in the toric case [342, 343], we expect many interesting connection with topological string theory, such as topological vertex [344].”
Gromov–Witten theory and Donaldson–Thomas theory, I (2003, background): “Insertions in the Gromov–Witten theory of X are determined by primary and descendent fields.”