Year: 2026
Type: preprint
Abstract: We construct connected spectral curves for semisimple conformal Frobenius manifolds with flat unit, using the periods of the second structure equation. Eynard-Orantin topological recursion on these curves reproduces the stable ancestor correlators of Givental-Teleman reconstruction. The spectral curves are defined on simply connected domains in the complex plane. We apply the construction to the quantum cohomology of $\mathbb P^n$ for $n\ge2$ at a point, obtaining explicit spectral curve data in terms of Hecke triangle groups and hypergeometric functions. Finally, for $\mathbb P^2$ and $\mathbb P^3$, we express the complete spectral curve data, including the bidifferentials, in classical modular and quasimodular forms.
Source: arXiv (Cornell University)
Authors: Xiong, Dingkang, Zhou, Jian
Institution: Tsinghua University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223000812