Toric Amplitudes and Universal Adjoints
Algebraic Geometry
2026-01-14 v3 High Energy Physics - Theory
Combinatorics
Abstract
A toric amplitude is a rational function associated to a simplicial polyhedral fan. The definition is inspired by scattering amplitudes in particle physics. We prove algebraic properties of such amplitudes and study the geometry of their zero loci. These hypersurfaces play the role of Warren's adjoint via a dual volume interpretation. We investigate their Fano schemes and singular loci via the nef cone and toric irrelevant ideal of the fan.
Keywords
Cite
@article{arxiv.2504.00897,
title = {Toric Amplitudes and Universal Adjoints},
author = {Simon Telen},
journal= {arXiv preprint arXiv:2504.00897},
year = {2026}
}
Comments
to appear in the Journal of the London Mathematical Society