The tropical discriminant of a polynomial map on a plane
Algebraic Geometry
2022-09-14 v3 Combinatorics
Abstract
The discriminant of a polynomial map is central to problems from affine geometry and singularity theory. Standard methods for characterizing it rely on elimination techniques that can often be ineffective. This paper concerns polynomial maps on the two-dimensional torus defined over a field of Puiseux series. We present a combinatorial procedure for computing the tropical curve of the discriminant of maps determined by generic polynomials with given supports. Our results enable one to compute the Newton polytope of the discriminant of complex polynomial maps on the plane.
Cite
@article{arxiv.2202.05052,
title = {The tropical discriminant of a polynomial map on a plane},
author = {Boulos El Hilany},
journal= {arXiv preprint arXiv:2202.05052},
year = {2022}
}
Comments
Minor revision on the introduction. 29 pages, 14 figures, one Appendix. Comments are welcome!