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36
GromovWitten/DonaldsonThomas correspondence for toric 3folds
, 2008
"... We prove the equivariant GromovWitten theory of a nonsingular toric 3fold X with primary insertions is equivalent to the equivariant DonaldsonThomas theory of X. As a corollary, the topological vertex calculations by Agangic, Klemm, Mariño, and Vafa of the GromovWitten theory of local CalabiYau ..."
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Cited by 60 (17 self)
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We prove the equivariant GromovWitten theory of a nonsingular toric 3fold X with primary insertions is equivalent to the equivariant DonaldsonThomas theory of X. As a corollary, the topological vertex calculations by Agangic, Klemm, Mariño, and Vafa of the GromovWitten theory of local CalabiYau toric 3folds are proven to be correct in the full 3leg setting.
Localization and gluing of orbifold amplitudes: the GromovWitten orbifold vertex
, 2012
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The Crepant Resolution Conjecture in all genera for type A singularities
, 2008
"... We prove an all genera version of the Crepant Resolution Conjecture of Ruan and BryanGraber for type A surface singularities. We are based on a method that explicitly computes HurwitzHodge integrals described in an earlier paper and some recent results by LiuXu for some intersection numbers on t ..."
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Cited by 14 (2 self)
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We prove an all genera version of the Crepant Resolution Conjecture of Ruan and BryanGraber for type A surface singularities. We are based on a method that explicitly computes HurwitzHodge integrals described in an earlier paper and some recent results by LiuXu for some intersection numbers on the DeligneMumford moduli spaces. We also generalize our results to some threedimensional orbifolds.
THE LOCAL GROMOVWITTEN INVARIANTS OF CONFIGURATIONS OF RATIONAL CURVES
, 2005
"... ABSTRACT. We compute the local GromovWitten invariants of certain configurations of rational curves in a CalabiYau threefold. These configurations are connected subcurves of the “minimal trivalent configuration”, which is a particular tree of P 1 ’s with specified formal neighborhood. We show that ..."
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Cited by 14 (3 self)
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ABSTRACT. We compute the local GromovWitten invariants of certain configurations of rational curves in a CalabiYau threefold. These configurations are connected subcurves of the “minimal trivalent configuration”, which is a particular tree of P 1 ’s with specified formal neighborhood. We show that these local invariants are equal to certain global or ordinary GromovWitten invariants of a blowup of P 3 at points, and we compute these ordinary invariants using the geometry of the Cremona transform. We also realize the configurations in question as formal toric schemes and compute their formal GromovWitten invariants using the mathematical and physical theories of the topological vertex. In particular, we provide further evidence equating the vertex amplitudes derived from physical and mathematical theories of the topological vertex. 1.
D.: Open GromovWitten theory and the crepant resolution conjecture
 Michigan Math. J
, 2012
"... Abstract. We compute open GW invariants for KP1 ⊕OP1, open orbifold GW invariants for [C3/Z2], formulate an open crepant resolution conjecture and verify it for this pair. We show that open invariants can be glued together to deduce the BryanGraber closed crepant resolution conjecture for the orb ..."
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Cited by 10 (5 self)
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Abstract. We compute open GW invariants for KP1 ⊕OP1, open orbifold GW invariants for [C3/Z2], formulate an open crepant resolution conjecture and verify it for this pair. We show that open invariants can be glued together to deduce the BryanGraber closed crepant resolution conjecture for the orbifold [OP1(−1)⊕OP1(−1)/Z2] and its crepant resolution KP1×P1.
Formulae of onepartition and twopartition Hodge integrals
, 2006
"... Prompted by the duality between open string theory on noncompact Calabi–Yau threefolds and Chern–Simons theory on threemanifolds, M Mariño and C Vafa conjectured a formula of onepartition Hodge integrals in term of invariants of the unknot. Many Hodge integral identities, including the λg conjectu ..."
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Cited by 9 (1 self)
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Prompted by the duality between open string theory on noncompact Calabi–Yau threefolds and Chern–Simons theory on threemanifolds, M Mariño and C Vafa conjectured a formula of onepartition Hodge integrals in term of invariants of the unknot. Many Hodge integral identities, including the λg conjecture and the ELSV formula, can be obtained by taking limits of the Mariño–Vafa formula. Motivated by the Mariño–Vafa formula and formula of Gromov–Witten invariants of local toric Calabi–Yau threefolds predicted by physicists, J Zhou conjectured a formula of twopartition Hodge integrals in terms of invariants of the Hopf link and used it to justify the physicists ’ predictions. In this expository article, we describe proofs and applications of these two formulae of Hodge integrals based on joint works of K Liu, J Zhou and the author. This is an expansion of the author’s talk of the same title at the BIRS workshop The