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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
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 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
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.
Spin GromovWitten invariants
 Comm. Math. Phys
"... Abstract. We dene and study rspin GromovWitten invariants and rspin quantum cohomology of a projective variety V, where r 2 is an integer. The main element of the construction is the space M 1=r g;n(V) of rspin maps, the stable maps into a variety V from npointed algebraic curves of genus g wi ..."
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with the additional data of an rspin structure on the curve. We prove that M 1=r g;n(V) is a DeligneMumford stack and use it to dene the rspin GromovWitten classes of V. We show that these classes yield a cohomological eld theory (CohFT) which is isomorphic to the tensor product of the CohFT as
Symplectic GromovWitten Invariants
"... The theory of GromovWitten invariants has its origins in Gromov’s pioneering work. Encouraged by conjectures coming from physicists, it took a while until a rigorous mathematical foundation was laid. The aim of this short survey is to present some of the results of the last decade concerning this f ..."
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Cited by 1 (1 self)
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The theory of GromovWitten invariants has its origins in Gromov’s pioneering work. Encouraged by conjectures coming from physicists, it took a while until a rigorous mathematical foundation was laid. The aim of this short survey is to present some of the results of the last decade concerning
Results 1  10
of
1,295,006