Proudfoot-Speyer degenerations of scattering equations

TL;DR

This paper introduces a new algebraic and geometric approach to solving scattering equations using degenerations, with a focus on hyperplane arrangements and computational algorithms.

Contribution

It formulates scattering equations as linear problems on reciprocal linear spaces and develops a degeneration-based homotopy algorithm for their solution.

Findings

Developed a homotopy algorithm for scattering equations

Analyzed Hilbert regularity of related ideals

Applied methods to CHY scattering equations

Abstract

We study scattering equations of hyperplane arrangements from the perspective of combinatorial commutative algebra and numerical algebraic geometry. We formulate the problem as linear equations on a reciprocal linear space and develop a degeneration-based homotopy algorithm for solving them. We investigate the Hilbert regularity of the corresponding homogeneous ideal and apply our methods to CHY scattering equations.