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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
GromovWitten classes, quantum cohomology, and enumerative geometry
 Commun. Math. Phys
, 1994
"... The paper is devoted to the mathematical aspects of topological quantum field theory and its applications to enumerative problems of algebraic geometry. In particular, it contains an axiomatic treatment of Gromov–Witten classes, and a discussion of their properties for Fano varieties. Cohomological ..."
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Cited by 473 (3 self)
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The paper is devoted to the mathematical aspects of topological quantum field theory and its applications to enumerative problems of algebraic geometry. In particular, it contains an axiomatic treatment of Gromov–Witten classes, and a discussion of their properties for Fano varieties. Cohomological
HAMILTONIAN GROMOV–WITTEN INVARIANTS
, 2000
"... In this paper we introduce invariants of semifree Hamiltonian actions of S¹ on compact symplectic manifolds (which satisfy some technical conditions related to positivity) using the space of solutions to certain gauge theoretical equations. These equations generalize at the same time the vortex equ ..."
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equations and the holomorphicity equation used in Gromov–Witten theory. In the definition of the invariants we combine ideas coming from gauge theory and the ideas underlying the construction of Gromov–Witten invariants.
The local Gromov–Witten invariants of
"... arXiv version: fonts, pagination and layout may vary from GT published version ..."
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Cited by 2 (0 self)
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arXiv version: fonts, pagination and layout may vary from GT published version
The Virasoro conjecture for Gromov–Witten invariants
, 1998
"... The Virasoro conjecture is a conjectured sequence of relations among the descendent GromovWitten invariants of a smooth projective variety in all genera; the only varieties for which it is known to hold are a point (Kontsevich) and CalabiYau manifolds of dimension at least three. We review the s ..."
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Cited by 34 (1 self)
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The Virasoro conjecture is a conjectured sequence of relations among the descendent GromovWitten invariants of a smooth projective variety in all genera; the only varieties for which it is known to hold are a point (Kontsevich) and CalabiYau manifolds of dimension at least three. We review
GromovWitten invariants of symplectic sums
"... The natural sum operation for symplectic manifolds is defined by gluing along codimension two submanifolds. Specifically, let X be a symplectic 2nmanifold with a symplectic (2n − 2)submanifold V. Given a similar pair (Y,V) with a symplectic identification V = V and a complex antilinear isomorphism ..."
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Cited by 33 (4 self)
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linear isomorphism between the normal bundles of V and V, we can form the symplectic sum Z = X# V =V Y. This note announces a general formula for computing the GromovWitten invariants of the sum Z in terms of relative GromovWitten invariants of (X,V) and (Y,V). Section 1 is a review of the GW invariants
GROMOVWITTEN THEORY OF PRODUCT STACKS
, 2009
"... Let X1 and X2 be smooth proper DeligneMumford stacks with projective coarse moduli spaces. We prove a formula for orbifold GromovWitten invariants of the product stack X1 × X2 in terms of GromovWitten invariants of the factors X1 and X2. As an application, we deduce a decomposition result for Gro ..."
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Cited by 8 (3 self)
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Let X1 and X2 be smooth proper DeligneMumford stacks with projective coarse moduli spaces. We prove a formula for orbifold GromovWitten invariants of the product stack X1 × X2 in terms of GromovWitten invariants of the factors X1 and X2. As an application, we deduce a decomposition result
GromovWitten theory of Anresolutions
, 2008
"... We give a complete solution for the reduced GromovWitten theory of resolved surface singularities of type An, for any genus, with arbitrary descendent insertions. We also present a partial evaluation of the Tequivariant relative GromovWitten theory of the threefold An × P 1 which, under a nondege ..."
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Cited by 6 (0 self)
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We give a complete solution for the reduced GromovWitten theory of resolved surface singularities of type An, for any genus, with arbitrary descendent insertions. We also present a partial evaluation of the Tequivariant relative GromovWitten theory of the threefold An × P 1 which, under a
Results 1  10
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643,984