Gromov–Witten theory and Donaldson–Thomas theory, I

By Davesh Maulik, N. Nekrasov, A. Okounkov, R. Pandharipande. Compositio Mathematica, 2003

596 citations recorded by the source corpus.

We conjecture an equivalence between the Gromov–Witten theory of 3-folds and the holomorphic Chern–Simons theory of Donaldson and Thomas. For Calabi–Yau 3-folds, the equivalence is defined by the change of variables $e^{iu}=-q$, where $u$ is the genus parameter of Gromov–Witten theory and $q$ is the Euler characteristic parameter of Donaldson–Thomas theory. The conjecture is proven for local Calabi–Yau toric surfaces.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c0954924e7b170f477cb723f4d1100e7c4652e8b

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Citations in the corpus

Good degeneration of Quot-schemes and coherent systems (2011, methodology): “nsion zero part of the term inside the bracket. The partition function is Zd X;q Yr i=1 τ˜ki(γi) = X n∈Z deg DYr i=1 ˜τki(γi) Ed·v+n X qn. The commonly used form of DT-invariants as introduced in [MNOP06], uses the moduli In(X,β) of ideal sheaves of subschemes Z⊂ Xwith ﬁxed curve class β= [Z]. In ”
Deformation-obstruction theory for complexes via Atiyah and Kodaira–Spencer classes (2008, background): “ii) is automatic is for arbitrary threefolds and complexes satisfying (ii′) Hom0(E,E) = OX b and Exti(E,E) = 0, i<0. This implies both (ii) and that Eis simple, and applies to the ideal sheaves of [15, 17] and the complexes I• of [16]. 4.4. The rank zero case. When rk(E) = 0 we consider simple co”
Topological M-theory as unification of form theories of gravity (2004, background): “or, equivalently, as a sum over ideal sheaves [46].”
Curves on K3 surfaces and modular forms (2010, methodology): “a Laurent series WP µ (q;s1,s2,s3) ∈ Q(s1,s2,s3)((q)). Lemma 22. The qn coeﬃcient of WP µ is divisible by s1 +s2 for n>|µ|. Proof. The proof here is nearly identical to the calculation in [43] and [31] with a slightly diﬀerent combinatorial formula. We again follow notation from [47]. CURVES ON K”
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].”
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].”
Symmetric Obstruction Theories and Hilbert Schemes of Points on Threefolds (2005, methodology): “(c) This is an immediate consequence of [Maulik et al. 2003], Theorem 2 in § 4.”
The moduli space of stable quotients (2009, background): “New compactifications of classical spaces arise naturally: a nonsingular and irreducible compactification of the moduli of maps from genus 1 curves to projective space is obtained.”