The j-invariant of a plane tropical cubic
Algebraic Geometry
2009-07-28 v1 Combinatorics
Abstract
Several results in tropical geometry have related the j-invariant of an algebraic plane curve of genus one to the cycle length of a tropical curve of genus one. In this paper, we prove that for a plane cubic over the field of Puiseux series the negative of the generic valuation of the -invariant is equal to the cycle length of the tropicalization of the curve, if there is a cycle at all.
Keywords
Cite
@article{arxiv.0709.3785,
title = {The j-invariant of a plane tropical cubic},
author = {Eric Katz and Hannah Markwig and Thomas Markwig},
journal= {arXiv preprint arXiv:0709.3785},
year = {2009}
}
Comments
The proofs rely partly on computations done with polymake, topcom and Singular