Advanced Studies in Pure Mathematics

Big $I$-functions

Ionuţ Ciocan-Fontanine and Bumsig Kim

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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

Source
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

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

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1538622435

Digital Object Identifier
doi:10.2969/aspm/06910323

Mathematical Reviews number (MathSciNet)
MR3586512

Zentralblatt MATH identifier
1369.14018

Subjects
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]

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


Export citation