Numerical homotopies from Khovanskii bases
Algebraic Geometry
2020-09-01 v1
Abstract
We present numerical homotopy continuation algorithms for solving systems of equations on a variety in the presence of a finite Khovanskii basis. These take advantage of Anderson's flat degeneration to a toric variety. When Anderson's degeneration embeds into projective space, our algorithm is a special case of a general toric two-step homotopy algorithm. When Anderson's degeneration is embedded in a weighted projective space, we explain how to lift to a projective space and construct an appropriate modification of the toric homotopy. Our algorithms are illustrated on several examples using Macaulay2.
Cite
@article{arxiv.2008.13055,
title = {Numerical homotopies from Khovanskii bases},
author = {Michael Burr and Frank Sottile and Elise Walker},
journal= {arXiv preprint arXiv:2008.13055},
year = {2020}
}
Comments
20 pages, 3 figures