منابع مشابه
Relative Gromov - Witten invariants
We define relative Gromov-Witten invariants of a symplectic manifold relative to a codimension-two 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 ‘V -stable’ maps. Simple special cases include the Hurwitz numbers for algebraic curves and the enumerative invariants of Caporaso and Ha...
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We define tropical Psi-classes on M 0,n (R 2 , d) and consider intersection products of Psi-classes and pull-backs of evaluations on this space. We show a certain WDVV equation which is sufficient to prove that tropical numbers of curves satisfying certain Psi-and evaluation conditions are equal to the corresponding classical numbers. We present an algorithm that generalizes Mikhalkin's lattice...
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The group (Z/nZ) is shown to act on the Gromov-Witten invariants of the complex flag manifold. We also deduce several corollaries of this result.
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We prove that any three-point genus zero Gromov-Witten invariant on a type A Grassmannian is equal to a classical intersection number on a two-step flag variety. We also give symplectic and orthogonal analogues of this result; in these cases the two-step flag variety is replaced by a sub-maximal isotropic Grassmannian. Our theorems are applied, in type A, to formulate a conjectural quantum Litt...
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Given a closed orientable Lagrangian surface L in a closed symplectic four-manifold (X,ω) together with a relative homology class d ∈ H2(X,L;Z) with vanishing boundary in H1(L;Z), we prove that the algebraic number of J-holomorphic discs with boundary on L, homologous to d and passing through the adequate number of points neither depends on the choice of the points nor on the generic choice of ...
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ژورنال
عنوان ژورنال: Journal of the American Mathematical Society
سال: 2012
ISSN: 0894-0347,1088-6834
DOI: 10.1090/s0894-0347-2012-00757-7