Stable quasimaps to GIT quotients

By Ionut Ciocan-Fontanine, Bumsig Kim, Davesh Maulik. 2011

225 citations recorded by the source corpus.

We construct new compactifications with good properties of moduli spaces of maps from nonsingular marked curves to a large class of GIT quotients. This generalizes from a unified perspective many particular examples considered earlier in the literature.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/54e214f70a324515c1e0f2f6d8b1ec8f9d4b47a0

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Wall-crossing in genus zero quasimap theory and mirror maps (2013, background): “arieties, as well as zero loci of sections of homogeneous bundles on them, local targets with base a GIT quotient, Nakajima quiver varieties etc. See §2.8 for a list and more details. As explained in [CKM], one has in fact a Cohomological Field Theory in the sense of Kontsevich and Manin for each va”
Orbifold quasimap theory (2014, methodology): “This part is identical to the corresponding one in [12].”
Higher genus quasimap wall-crossing for semi-positive targets (2013, methodology): “er varieties. It follows that the T-ﬁxed loci in W//G and in all the moduli spaces of stable quasimaps are also proper. In this situation we get a T-equivariant version of the CohFT, see e.g. §6.3 in [CKM] and all results in §2.3 (which may be viewed as corresponding to the zero-dimensional torus T ”
QUANTUM KIRWAN MORPHISM AND GROMOV-WITTEN INVARIANTS OF QUOTIENTS I (2012, unknown): “See [10], [9] for more recent work.”
Lectures on K-theoretic computations in enumerative geometry (2015, background): “In general, [20] consider quasimaps to quotients X “ Y{G where Y is an affine algebraic variety with an action of a reductive group G such that ∅ ‰ YG-stable “ YG-semistable Ă Ynonsingular .”
Elliptic stable envelopes (2016, background): “plexities of K-theoretic curve counting only to the extent required to state and prove our results. We denote by QM(X) = {stable f: P1 99KX} ∼= the moduli space of stable quasimaps to Xas deﬁned in [17]. This is a countable union of algebraic varieties indexed by degf∈H2(X,Z)eﬀective . The standard”