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538
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
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 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
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 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 199 (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 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 34 (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
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
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
GromovWitten invariants of blowups
 J. Algebraic Geom
"... In the first part of the paper, we give an explicit algorithm to compute the (genus zero) GromovWitten invariants of blowups of an arbitrary convex projective variety in some points if one knows the GromovWitten invariants of the original variety. In the second part, we specialize to blowups of ..."
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Cited by 34 (1 self)
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In the first part of the paper, we give an explicit algorithm to compute the (genus zero) GromovWitten invariants of blowups of an arbitrary convex projective variety in some points if one knows the GromovWitten invariants of the original variety. In the second part, we specialize to blow
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
Results 1  10
of
538