Year: 2026
Type: preprint
Abstract: Let $G$ be a finite group admitting a rational fixed-point-free (FPF) representation $V$, with a $G$-invariant full-rank lattice $L\subset V$. We study the induced $G$-action on the complex torus $V_{\mathbb{C}}/L$ and the quotient orbifold $V_{\mathbb{C}}/(G\ltimes L)$. We prove that every FPF group admits a unique irreducible rational FPF representation. We derive closed-form formulas for three core geometric invariants: the number of non-free points of the torus action, the number of singular points of the quotient orbifold, and its orbifold Euler characteristic.
Source: arXiv (Cornell University)
Author: Zhang, Xue
Institution: China Agricultural University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214236974