The j-invariant of a plane tropical cubic

Details The j-invariant of a plane tropical cubic The j-invariant of a plane tropical cubic

2007-09-24

arxiv.org/abs/0709.3785v1

J. Algebra 320 (2008), no. 10, 3832--3848

Mathematics

Algebraic Geometry

The proofs rely partly on computations done with polymake, topcom and Singular

Scientific paper

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 $j$-invariant is equal to the cycle length of the tropicalization of the curve, if there is a cycle at all.

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