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Symmetries of GromovWitten Invariants
, 2000
"... The group (Z/nZ) 2 is shown to act on the GromovWitten invariants of the complex flag manifold. We also deduce several corollaries of this result. 1 ..."
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Cited by 3 (1 self)
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The group (Z/nZ) 2 is shown to act on the GromovWitten invariants of the complex flag manifold. We also deduce several corollaries of this result. 1
Minimal Gromov–Witten ring
 Izv. Math
"... Abstract. We build the abstract theory of Gromov–Witten invariants of genus 0 for quantum minimal Fano varieties (a minimal natural (with respect to Gromov– Witten theory) class of varieties). In particular, we consider “the minimal Gromov– Witten ring”, i. e. a commutative algebra with generators a ..."
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Cited by 4 (4 self)
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Abstract. We build the abstract theory of Gromov–Witten invariants of genus 0 for quantum minimal Fano varieties (a minimal natural (with respect to Gromov– Witten theory) class of varieties). In particular, we consider “the minimal Gromov– Witten ring”, i. e. a commutative algebra with generators
Relative GromovWitten invariants
 Ann. of Math
, 2003
"... We define relative GromovWitten invariants of a symplectic manifold relative to a codimensiontwo symplectic submanifold. These invariants are the key ingredients in the symplectic sum formula of [IP4]. The main step is the construction of a compact space of ‘Vstable ’ maps. Simple special cases i ..."
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Cited by 119 (10 self)
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We define relative GromovWitten invariants of a symplectic manifold relative to a codimensiontwo symplectic submanifold. These invariants are the key ingredients in the symplectic sum formula of [IP4]. The main step is the construction of a compact space of ‘Vstable ’ maps. Simple special cases
GromovWitten invariants in algebraic geometry
, 1996
"... GromovWitten invariants for arbitrary projective varieties and arbitrary genus are constructed using the techniques from [K. Behrend, B. Fantechi. The Intrinsic Normal Cone.] ..."
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Cited by 200 (2 self)
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GromovWitten invariants for arbitrary projective varieties and arbitrary genus are constructed using the techniques from [K. Behrend, B. Fantechi. The Intrinsic Normal Cone.]
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 474 (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.
GROMOVWITTEN INVARIANTS OF STABILIZATIONS OF
, 906
"... Abstract. We relate the GromovWitten invariants of X×S 2 to the SeibergWitten invariants of X where X is a simplyconnected symplectic 4manifold. We also give examples that expose the similarity between the classification of smooth 4manifolds and some classification problems regarding symplectic ..."
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Abstract. We relate the GromovWitten invariants of X×S 2 to the SeibergWitten invariants of X where X is a simplyconnected symplectic 4manifold. We also give examples that expose the similarity between the classification of smooth 4manifolds and some classification problems regarding
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 127 (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
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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Cited by 1 (0 self)
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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
GromovWitten invariants on Grassmannians
 J. AMER. MATH. SOC
, 2003
"... We prove that any threepoint genus zero GromovWitten invariant on a type A Grassmannian is equal to a classical intersection number on a twostep flag variety. We also give symplectic and orthogonal analogues of this result; in these cases the twostep flag variety is replaced by a submaximal i ..."
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Cited by 35 (5 self)
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We prove that any threepoint genus zero GromovWitten invariant on a type A Grassmannian is equal to a classical intersection number on a twostep flag variety. We also give symplectic and orthogonal analogues of this result; in these cases the twostep flag variety is replaced by a sub
Results 1  10
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2,834