## 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].

### MSC:

 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)

### Citations:

Zbl 1203.14014; Zbl 1282.14022
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