On a Relation between Spectral Theory of Lens Spaces and Ehrhart Theory
Differential Geometry
2016-03-18 v2 Algebraic Geometry
Abstract
In this article Ehrhart quasi-polynomials of simplices are employed to determine isospectral lens spaces in terms of a finite set of numbers. Using the natural lattice associated with a lens space the associated toric variety of a lens space is introduced. It is proved that if two lens spaces are isospectral then the dimension of global sections of powers of a natural line bundle on these two toric varieties are equal and they have the same general intersection number. Also, harmonic polynomial representation of the group SO(n) is used to provide a direct proof for a theorem of Lauret, Miatello and Rossetti on isospectrality of lens spaces.
Keywords
Cite
@article{arxiv.1601.04256,
title = {On a Relation between Spectral Theory of Lens Spaces and Ehrhart Theory},
author = {H. Mohades and B. Honari},
journal= {arXiv preprint arXiv:1601.04256},
year = {2016}
}