Advanced Studies in Pure Mathematics

Big $I$-functions

Ionuţ Ciocan-Fontanine and Bumsig Kim

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We introduce a new big $I$-function for certain GIT quotients $W/\!\!/\mathbf{G}$ using the quasimap graph space from infinitesimally pointed $\mathbb{P}^1$ to the stack quotient $[W/\mathbf{G}]$. This big $I$-function is expressible by the small $I$-function introduced in [6, 10]. The $I$-function conjecturally generates the Lagrangian cone of Gromov-Witten theory for $W/\!\!/\mathbf{G}$ defined by Givental. We prove the conjecture when $W/\!\!/\mathbf{G}$ has a torus action with good properties.

Article information

Development of Moduli Theory — Kyoto 2013, O. Fujino, S. Kondō, A. Moriwaki, M. Saito and K. Yoshioka, eds. (Tokyo: Mathematical Society of Japan, 2016), 323-347

Received: 29 January 2014
Revised: 23 May 2014
First available in Project Euclid: 4 October 2018

Permanent link to this document euclid.aspm/1538622435

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14D20: Algebraic moduli problems, moduli of vector bundles {For analytic moduli problems, see 32G13} 14D23: Stacks and moduli problems 14N35: Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants [See also 53D45]


Ciocan-Fontanine, Ionuţ; Kim, Bumsig. Big $I$-functions. Development of Moduli Theory — Kyoto 2013, 323--347, Mathematical Society of Japan, Tokyo, Japan, 2016. doi:10.2969/aspm/06910323.

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