Moduli stacks of stable toric quasimaps

By Ionut Ciocan-Fontanine, Bumsig Kim. 2009

105 citations recorded by the source corpus.

Abstract We construct new “virtually smooth” modular compactifications of spaces of maps from nonsingular curves to smooth projective toric varieties. They generalize Givental's compactifications, when the complex structure of the curve is allowed to vary and markings are included, and are the toric counterpart of the moduli spaces of stable quotients introduced by Marian, Oprea, and Pandharipande to compactify spaces of maps to Grassmannians. A brief discussion of the resulting invariants and their (conjectural) relation with Gromov–Witten theory is also included.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9c9f167a4bccb41da82bb478f55e5ea49b798bec

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Higher genus quasimap wall-crossing for semi-positive targets (2013, methodology): “triple (Cn+r,G,θ) is given by the same formula (5.9.1) Ism(q,z) = 1 + X β6=0 qβ nY+r ρ=1 Q0 j=−∞(c T 1 (Lρ) +jz) Qd ρ j=−∞(c T 1 (Lρ) +jz) , as it can be easily seen that the computation from §7.2 of [CK1] works for all GIT presentations. Recall that the class β runs over Eﬀ(Cn+r,G,θ) and d ρ= β(ξρ)”
Stable quasimaps to GIT quotients (2011, methodology): “The stability condition we consider initially generalizes the ones from [35], [10] and we call the resulting objects stable quasimaps toW/G.”
Wall-crossing in genus zero quasimap theory and mirror maps (2013, methodology): “= cont(k,β)(z) := 1, (k,β) = (0,0), z, (k,β) = (1,0), z(z−ψ•), otherwise, where zdenotes the generator of A∗ C∗(Spec(C)). The formula (4.2.1) is well-known, see e.g., [G2] for stable maps and [CK1], [CKM] for quasimaps. Note that it is the same for all targets W//G. In addition, we observe that i”
Orbifold quasimap theory (2014, methodology): “The theory of ε-stable quasimaps to a large class of GIT quotient targets was developed in [12], generalizing and unifying the earlier works [26, 8, 28, 30].”