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="https://arxiv.org/abs/0709.3785v1">arXiv:0709.3785v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2lz52ojuwnavre4q3hzt43m75e">fatcat:2lz52ojuwnavre4q3hzt43m75e</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-0709.3785/0709.3785.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> File Archive [PDF] </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/0709.3785v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>