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The j-invariant of a plane tropical cubic
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<span title="2007-09-24">2007</span>
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arXiv
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<span class="release-stage" >pre-print</span>
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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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