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We relate the genus zero gauged Gromov-Witten invariants of a smooth projective variety for sufficiently small area with equivariant Gromov-Witten invariants. As an application we deduce a gauged version of abelianiza-tion for Gromov-Witten invariants in the small area chamber. In the symplectic setting, we prove that any sequence of genus zero symplectic… (More)

This article deals with efficiency improvement and how to identify appropriate benchmarks for inefficient firms to imitate. We argue that the most relevant benchmark is the most similar efficient firm. Having interpreted similarity in terms of input endowments, the problem reduces to find the closest reference firm on the efficient subset of the isoquant.… (More)

- Eduardo Gonzalez
- 2005

In this paper we describe a method to establish when a symplectic 6-manifold M with semi-free Hamiltonian S 1-action is unique up to isomor-phism (equivariant symplectomorphism). This method will rely on a study of the symplectic geometry of the reduced spaces and a gluing procedure along regular levels. We prove that if the reduced spaces satisfy a… (More)

We give a quantum version of the Danilov-Jurkiewicz presentation of the cohomology of a compact toric orbifold with projective coarse moduli space. More precisely, we construct a canonical isomorphism from a formal version of the Batyrev ring from [5] to the quantum orbifold cohomology in a formal neighborhood of a canonical bulk deformation. This… (More)

We study the variation of the moduli space of symplectic vortices on a fixed holomorphic curve with respect to the area form. For compact, convex varieties we define symplectic vortex invariants and prove a wall-crossing formula for them. As an application, we prove a vortex version of the abelianization conjecture of Bertram, Ciocan-Fontanine, and Kim [4],… (More)

We prove a quantum version of Kalkman's wall-crossing formula [34], [41] comparing intersection pairings on geometric invariant theory (git) quotients related by a change in polarization, under certain stable=semistable assumptions. The formula is the same, but each expression in the formula is quantized in the sense that it is replaced by an integral over… (More)

We prove a quantum version of the localization formula of Witten [58], see also [56], [50], [60], which relates invariants of a git quotient with the equi-variant invariants of the action. As an application, we prove a quantum version of an abelianization formula of S. Martin [38], relating invariants of geometric invariant theory quotients by a group and… (More)

We prove a gluing theorem for a symplectic vortex on a compact complex curve and a collection of holomorphic sphere bubbles. Using the theorem we show that the moduli space of regular strongly stable symplectic vortices on a fixed curve with varying markings has the structure of a stratified-smooth topo-logical orbifold. In addition, we show that the moduli… (More)

We prove properness of moduli stacks of gauged maps satisfying a stability conditition introduced by Mundet [42] and Schmitt [48]. The proof combines a git construction of Schmitt [48], properness for twisted stable maps by Abramovich-Vistoli [1], a variation of a bounded-ness argument due to Ciocan-Fontanine-Kim-Maulik [13], and a removal of singularities… (More)