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The degree of the variety of rational ruled surfaces and Gromov-Witten invariants  [PDF]
Cristina Martinez Ramirez
Mathematics , 2006,
Abstract: We compute the degree of the variety parametrizing rational ruled surfaces of degree d in the projective space by relating the problem to Gromov-Witten invariants and Quantum cohomology.
Gromov Witten invariants of exploded manifolds  [PDF]
Brett Parker
Mathematics , 2011,
Abstract: This paper describes the structure of the moduli space of holomorphic curves and constructs Gromov Witten invariants in the category of exploded manifolds. This includes defining Gromov Witten invariants relative to normal crossing divisors and proving the associated gluing theorem which involves summing relative invariants over a count of tropical curves.
The product formula for Gromov-Witten invariants  [PDF]
Kai Behrend
Mathematics , 1997,
Abstract: We prove that the system of Gromov-Witten invariants of the product of two varieties is equal to the tensor product of the systems of Gromov-Witten invariants of the two factors.
Symmetries of Gromov-Witten invariants  [PDF]
Alexander Postnikov
Mathematics , 2000,
Abstract: The group (Z/nZ)^2 is shown to act on the Gromov-Witten invariants of the complex flag manifold. We also deduce several corollaries of this result.
Gromov-Witten invariants for varieties with C* action  [PDF]
Anca Mustata,Andrei Mustata
Mathematics , 2015,
Abstract: For any smooth projective variety with a C* action, we reduce the problem of computing its Gromov-Witten invariants to the similar problem for its fixed locus. Starting from the stacky version of variation of GIT for our variety, we construct the building blocks for the fixed loci of the moduli space of stable maps. We use this construction to compute their contribution to the virtual fundamental class.
Gromov-Witten invariants of stable maps with fields  [PDF]
Huai-liang Chang,Jun Li
Mathematics , 2011,
Abstract: We construct the Gromov-Witten invariants of moduli of stable morphisms to $\Pf$ with fields. This is the all genus mathematical theory of the Guffin-Sharpe-Witten model, and is a modified twisted Gromov-Witten invariants of $\Pf$. These invariants are constructed using the cosection localization of Kiem-Li, an algebro-geometric analogue of Witten's perturbed equations in Landau-Ginzburg theory. We prove that these invariants coincide, up to sign, with the Gromov-Witten invariants of quintics.
Hamiltonian Gromov-Witten invariants  [PDF]
Ignasi Mundet i Riera
Mathematics , 2000,
Abstract: In this paper we introduce invariants of semi-free Hamiltonian actions of $S\sp 1$ 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 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. This paper is based on a part of my PhD Thesis (see math/9912150).
Relative Gromov-Witten Invariants  [PDF]
Eleny-Nicoleta Ionel,Thomas H. Parker
Mathematics , 1999,
Abstract: 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 Harris.
Virtual moduli cycles and Gromov-Witten invariants of general symplectic manifolds  [PDF]
Jun Li,Gang Tian
Mathematics , 1996,
Abstract: We construct Gromov-Witten invariants of general symplectic manifolds.
Stationary Gromov-Witten invariants of projective spaces  [PDF]
Paul Norbury
Mathematics , 2011,
Abstract: We represent stationary descendant Gromov-Witten invariants of projective space, up to explicit combinatorial factors, by polynomials. One application gives the asymptotic behaviour of large degree behaviour of stationary descendant Gromov-Witten invariants in terms of intersection numbers over the moduli space of curves. We also show that primary Gromov-Witten invariants are "virtual" stationary descendants and hence the string and divisor equations can be understood purely in terms of stationary invariants.
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