The j-invariant of a plane tropical cubic [article]

Eric Katz, Hannah Markwig, Thomas Markwig
<span title="2007-09-24">2007</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
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.
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="">arXiv:0709.3785v1</a> <a target="_blank" rel="external noopener" href="">fatcat:2lz52ojuwnavre4q3hzt43m75e</a> </span>
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