English

The level structure in quantum K-theory and mock theta functions

Algebraic Geometry 2019-06-18 v2

Abstract

This is the first in a sequence of papers to develop the theory of levels in quantum K-theory and study its applications. Our main results in this paper are toric mirror theorems for permutation-equivariant quantum K-theory with level structure. In some of the simplest examples, we see the surprising appearance of Ramanujan's mock theta functions.

Keywords

Cite

@article{arxiv.1804.06552,
  title  = {The level structure in quantum K-theory and mock theta functions},
  author = {Yongbin Ruan and Ming Zhang},
  journal= {arXiv preprint arXiv:1804.06552},
  year   = {2019}
}

Comments

There was a gap in the previous proof of the mirror theorem using the wall-crossing approach. We rewrote Section 4 and prove the toric mirror theorems using the adelic characterization developed by Givental-Tonita; additional changes to Section 2.3 (properties of the level structure); typos fixed; some references added

R2 v1 2026-06-23T01:27:11.671Z