Advances in Theoretical and Mathematical Physics

Volume 23 (2019)

Number 3

Some applications of the mirror theorem for toric stacks

Pages: 767 – 802

DOI: https://dx.doi.org/10.4310/ATMP.2019.v23.n3.a4

Authors

Tom Coates (Department of Mathematics, Imperial College London, United Kingdom)

Alessio Corti (Department of Mathematics, Imperial College London, United Kingdom)

Hiroshi Iritani (Department of Mathematics, Graduate School of Science, Kyoto University, Sakyo-ku, Kyoto, Japan)

Hsian-Hua Tseng (Department of Mathematics, Ohio State University, Columbus, Oh., U.S.A.)

Abstract

We use the mirror theorem for toric Deligne–Mumford stacks, proved recently by the authors and by Cheong–Ciocan-Fontanine–Kim, to compute genus-zero Gromov–Witten invariants of a number of toric orbifolds and gerbes. We prove a mirror theorem for a class of complete intersections in toric Deligne–Mumford stacks, and use this to compute genus-zero Gromov–Witten invariants of an orbifold hypersurface.

Published 4 December 2019