Orbifold quasimap theory

D Cheong, I Ciocan-Fontanine, B Kim - Mathematische Annalen, 2015 - Springer
We extend to orbifolds the quasimap theory of Ciocan-Fontanine and Kim (Adv Math 225 (6):
3022–3051, 2010; J Geom Phys 75: 17–47, 2014) as well as the genus zero wall-crossing …

Quasimap wall-crossings and mirror symmetry

I Ciocan-Fontanine, B Kim - Publications mathématiques de l'IHÉS, 2020 - Springer
We state a wall-crossing formula for the virtual classes of ε ε-stable quasimaps to GIT
quotients and prove it for complete intersections in projective space, with no positivity …

[HTML][HTML] Stable quotients and the holomorphic anomaly equation

H Lho, R Pandharipande - Advances in Mathematics, 2018 - Elsevier
We study the fundamental relationship between stable quotient invariants and the B-model
for local P 2 in all genera. Our main result is a direct geometric proof of the holomorphic …

Quasimap wall-crossing for GIT quotients

Y Zhou - Inventiones mathematicae, 2022 - Springer
In this paper, we prove a wall-crossing formula for ϵ ϵ-stable quasimaps to GIT quotients
conjectured by Ciocan-Fontanine and Kim, for all targets in all genera, including the orbifold …

Mirror theorem for elliptic quasimap invariants

B Kim, H Lho - Geometry & Topology, 2018 - msp.org
We propose and prove a mirror theorem for the elliptic quasimap invariants of smooth Calabi–
Yau complete intersections in projective spaces. This theorem, combined with the wall …

The Abelian–Nonabelian Correspondence for I-Functions

R Webb - International Mathematics Research Notices, 2023 - academic.oup.com
We prove the abelian–nonabelian correspondence for quasimap-functions. That is, if is an
affine lci variety with an action by a complex reductive group, we prove an explicit formula …

The Abelian/Nonabelian Correspondence and Gromov–Witten Invariants of Blow-Ups

T Coates, W Lutz, Q Shafi - Forum of Mathematics, Sigma, 2022 - cambridge.org
We prove the abelian/nonabelian correspondence with bundles for target spaces that are
partial flag bundles, combining and generalising results by Ciocan-Fontanine–Kim–Sabbah …

Quantum Kirwan morphism and Gromov-Witten invariants of quotients I

CT Woodward - Transformation Groups, 2015 - Springer
This is the first in a sequence of papers in which we construct a quantum version of the
Kirwan map from the equivariant quantum cohomology QH G (X) of a smooth polarized …

Quantum Kirwan morphism and Gromov–Witten invariants of quotients III

CT Woodward - Transformation Groups, 2015 - Springer
This is the third in a sequence of papers in which we construct a quantum version of the
Kirwan map from the equivariant quantum cohomology QH G (X) of a smooth polarized …

Higher-genus quasimap wall-crossing via localization

E Clader, F Janda, Y Ruan - arXiv preprint arXiv:1702.03427, 2017 - arxiv.org
We give a new proof of Ciocan-Fontanine and Kim's wall-crossing formula relating the virtual
classes of the moduli spaces of $\epsilon $-stable quasimaps for different $\epsilon $ in any …