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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 484 (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
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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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
Normal forms of hierarchies of integrable PDEs, Frobenius manifolds and GromovWitten invariants
, 2001
"... We present a project of classification of a certain class of bihamiltonian 1+1 PDEs depending on a small parameter. Our aim is to embed the theory of Gromov Witten invariants of all genera into the theory of integrable systems. The project is focused at describing normal forms of the PDEs and their ..."
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Cited by 93 (2 self)
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We present a project of classification of a certain class of bihamiltonian 1+1 PDEs depending on a small parameter. Our aim is to embed the theory of Gromov Witten invariants of all genera into the theory of integrable systems. The project is focused at describing normal forms of the PDEs
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 123 (10 self)
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point in the DeligneMumford space Mg,n of curves, and evaluation at each marked point determines a point in X. Thus there is a map (0.1) Mg,n(X, A) → Mg,n × X n. The GromovWitten invariant of (X, ω)isthe homology class of the image for generic (J, ν). It depends only on the isotopy class
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
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.]
Hodge integrals and GromovWitten theory
 Invent. Math
"... Let Mg,n be the nonsingular moduli stack of genus g, npointed, DeligneMumford stable curves. For each marking i, there is an associated cotangent line bundle Li → Mg,n with fiber T ∗ C,pi over the moduli point [C, p1,...,pn]. Let ψi = c1(Li) ∈ H ∗ (Mg,n, Q). The integrals of products of the ψ cla ..."
The Cohomological Field Theory was propose by Kontsevich and
, 2002
"... Manin [5] for description of GromovWitten Classes. They prove that Cohomological Field Theory is equivalent to Formal Frobenius manifold. Formal Frobenius manifold is defined by a formal series F, satisfying ..."
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Manin [5] for description of GromovWitten Classes. They prove that Cohomological Field Theory is equivalent to Formal Frobenius manifold. Formal Frobenius manifold is defined by a formal series F, satisfying
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
Results 1  10
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3,356