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...
متن کاملGromov-witten Theory Learning Seminar
Today, Jonathan spoke, delivering an overview of Gromov-Witten theory and how associativity of quantum cohomology leads to applications in enumerative geometry. Today we always work over C, and follow Fulton-Pandharipande’s notes [FP96]. Classically, if X is a nonsingular projective variety and β ∈ H2(X;Z), we want to know how many algebraic curves in X represent the class β. This relates to ve...
متن کاملSymmetries of Gromov-Witten Invariants
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.
متن کاملGromov-Witten invariants on Grassmannians
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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ژورنال
عنوان ژورنال: Izvestiya: Mathematics
سال: 2008
ISSN: 1064-5632,1468-4810
DOI: 10.1070/im2008v072n06abeh002434