Gromov-Witten invariants for abelian and nonabelian quotients

By Aaron Bertram, Ionut Ciocan-Fontanine, Bumsig Kim. 2004

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Let X be a smooth projective variety over C with the (linearized) action of a complex reductive group G, and let T ⊂ G be a maximal torus. In this setting, there are two geometric invariant theory (GIT) quotients, X//T and X//G, with a rational map Φ : X//T − −> X//G between them. We will further assume that “stable = semistable” in the GIT and that all isotropy of stable points is trivial, so X//T and X//G are smooth projective varieties, and Φ is a G/T fibration.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2adb976093787ab096dbf7e959ce14b19af72111

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Citations in the corpus

Wall-crossing in genus zero quasimap theory and mirror maps (2013, background): “e O(−m) on Pn−1. Example 2.8.2. Type A ﬂag manifolds. These are also quotients of a vector space, but with G a product of GLk i (C)’s and θ given by the determinant character on each factor (see e.g. [BCK] for this quotient description). In particular, taking W = Hom(Cr,Cn) and G = GLr(C) with the o”
The Abelian/Nonabelian correspondence and Frobenius manifolds (2006, methodology): “Corollary 5.3.4 is a generalization of [ BCK2 , Conjecture 4.3] to the “big” parameter space.”
Stable quasimaps to GIT quotients (2011, background): “”, or “hyperquot schemes” on P1 of [28], see also [8], [22] are quasimap moduli spaces to ﬂag varieties of type A, viewed as GIT quotients of a vector space by a product of GL’s, as described e.g. in [4]. 50 IONUT¸ CIOCAN-FONTANINE, BUMSIG KIM, AND DAVESH MAULIK •Consider the vector space V := Hom(C”
QUANTUM KIRWAN MORPHISM AND GROMOV-WITTEN INVARIANTS OF QUOTIENTS I (2012, unknown): “See [10], [9] for more recent work.”
Higher genus quasimap wall-crossing for semi-positive targets (2013, methodology): “proof 56 IONUT¸ CIOCAN-FONTANINE AND BUMSIG KIM of Theorem 1.3.4 as well. Note that explicit closed formulas for the small I-functions of these targets are easily obtained from the results in [BCK1], [BCK2], [CKS]. For example, the T-equivariant small Ifor the local Grass(r,n) is Ism= 1 + X d>0 q”