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GIVENTAL’S LAGRANGIAN CONE AND S 1EQUIVARIANT GROMOV–WITTEN THEORY
, 2007
"... Abstract. In the approach to Gromov–Witten theory developed by Givental, genuszero Gromov–Witten invariants of a manifold X are encoded by a Lagrangian cone in a certain infinitedimensional symplectic vector space. We give a construction of this cone, in the spirit of S 1equivariant Floer theory, ..."
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Cited by 5 (4 self)
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Abstract. In the approach to Gromov–Witten theory developed by Givental, genuszero Gromov–Witten invariants of a manifold X are encoded by a Lagrangian cone in a certain infinitedimensional symplectic vector space. We give a construction of this cone, in the spirit of S 1equivariant Floer theory
THE 2TODA HIERARCHY AND THE EQUIVARIANT GROMOV–WITTEN THEORY OF CP 1
, 2005
"... Abstract. The equivariant Toda conjecture says that the equivariant Gromov– Witten invariants of CP 1 are governed by the flows of the 2Toda hierarchy. The 2Toda flows can be presented on the bosonic Fock space C[[yi, y j  i, j ≥ 0]] via vertex operators and Hirota quadratic equations (shortly HQ ..."
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Abstract. The equivariant Toda conjecture says that the equivariant Gromov– Witten invariants of CP 1 are governed by the flows of the 2Toda hierarchy. The 2Toda flows can be presented on the bosonic Fock space C[[yi, y j  i, j ≥ 0]] via vertex operators and Hirota quadratic equations (shortly
On the equivariant GromovWitten Theory of P 2bundles over curves
, 2008
"... We compute section class relative equivariant GromovWitten invariants of the total space of P 2bundles of the form P(O ⊕ L1 ⊕ L2) → C, where C is a genus g curve, and O is the trivial bundle, and L1 (resp. L2) is an arbitrary line bundle of degree k1 (resp. k2) over C. We prove a gluing formula f ..."
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Cited by 1 (0 self)
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We compute section class relative equivariant GromovWitten invariants of the total space of P 2bundles of the form P(O ⊕ L1 ⊕ L2) → C, where C is a genus g curve, and O is the trivial bundle, and L1 (resp. L2) is an arbitrary line bundle of degree k1 (resp. k2) over C. We prove a gluing formula
The local GromovWitten theory of curves
, 2008
"... We study the equivariant GromovWitten theory of a rank 2 vector bundle N over a nonsingular curve X of genus g: (i) We define a TQFT using the GromovWitten partition functions. The full theory is determined in the TQFT formalism from a few exact calculations. We use a reconstruction result proven ..."
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Cited by 38 (9 self)
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We study the equivariant GromovWitten theory of a rank 2 vector bundle N over a nonsingular curve X of genus g: (i) We define a TQFT using the GromovWitten partition functions. The full theory is determined in the TQFT formalism from a few exact calculations. We use a reconstruction result proven
Equivariant GromovWitten invariants
 INTERNAT. MATH. RES. NOTICES
, 1996
"... The objective of this paper is to describe the construction and some applications of the equivariant counterpart to the GromovWitten (GW) theory, i.e., intersection theory on spaces of (pseudo) holomorphic curves in (almost) Kähler manifolds. Given a Killing action of a compact Lie group G on a co ..."
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Cited by 126 (10 self)
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The objective of this paper is to describe the construction and some applications of the equivariant counterpart to the GromovWitten (GW) theory, i.e., intersection theory on spaces of (pseudo) holomorphic curves in (almost) Kähler manifolds. Given a Killing action of a compact Lie group G on a
The crepant resolution conjecture
, 2006
"... Abstract. For orbifolds admitting a crepant resolution and satisfying a hard Lefschetz condition, we formulate a conjectural equivalence between the GromovWitten theories of the orbifold and the resolution. We prove the conjecture for the equivariant GromovWitten theories of Sym n C 2 and Hilb n C ..."
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Cited by 42 (8 self)
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Abstract. For orbifolds admitting a crepant resolution and satisfying a hard Lefschetz condition, we formulate a conjectural equivalence between the GromovWitten theories of the orbifold and the resolution. We prove the conjecture for the equivariant GromovWitten theories of Sym n C 2 and Hilb n
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 Calabi
Results 1  10
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23,896