## Advanced Studies in Pure Mathematics

### Big $I$-functions

#### Abstract

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

Dates
Revised: 23 May 2014
First available in Project Euclid: 4 October 2018

https://projecteuclid.org/ euclid.aspm/1538622435

Digital Object Identifier
doi:10.2969/aspm/06910323

Mathematical Reviews number (MathSciNet)
MR3586512

Zentralblatt MATH identifier
1369.14018

#### Citation

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. https://projecteuclid.org/euclid.aspm/1538622435