Elliptic curves in honeycomb form
Algebraic Geometry
2012-03-13 v1 Combinatorics
Abstract
A plane cubic curve, defined over a field with valuation, is in honeycomb form if its tropicalization exhibits the standard hexagonal cycle. We explicitly compute such representations from a given j-invariant with negative valuation, we give an analytic characterization of elliptic curves in honeycomb form, and we offer a detailed analysis of the tropical group law on such a curve.
Keywords
Cite
@article{arxiv.1203.2356,
title = {Elliptic curves in honeycomb form},
author = {Melody Chan and Bernd Sturmfels},
journal= {arXiv preprint arXiv:1203.2356},
year = {2012}
}
Comments
20 pages, 5 figures