Big \(I\)-functions. (English) Zbl 1369.14018

Fujino, Osamu (ed.) et al., Development of moduli theory – Kyoto 2013. Proceedings of the 6th Mathematical Society of Japan-Seasonal Institute, MSJ-SI, Kyoto, Japan, June 11–21, 2013. Tokyo: Mathematical Society of Japan (MSJ) (ISBN 978-4-86497-032-7/hbk). Advanced Studies in Pure Mathematics 69, 323-347 (2016).
Summary: We introduce a new big \(I\)-function for certain GIT quotients \(W//G\) using the quasimap graph space from infinitesimally pointed \(\mathbb{P}^1\) to the stack quotient \([W/G]\). This big \(I\)-function is expressible by the small \(I\)-function introduced by the authors [Adv. Math. 225, No. 6, 3022–3051 (2010; Zbl 1203.14014) and the first author et al. [J. Geom. Phys. 75, 17–47 (2014; Zbl 1282.14022)]. The \(I\)-function conjecturally generates the Lagrangian cone of Gromov-Witten theory for \(W//G\) defined by Givental. We prove the conjecture when \(W//G\) has a torus action with good properties.
For the entire collection see [Zbl 1353.14002].


14D20 Algebraic moduli problems, moduli of vector bundles
14D23 Stacks and moduli problems
14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects)
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