Tropical complete intersection curves
Magnus Dehli Vigeland
TL;DR
This paper derives formulas for the number of vertices and the genus of tropical complete intersection curves, advancing the understanding of their combinatorial and topological properties.
Contribution
It provides explicit formulas for vertices and genus of tropical complete intersection curves, a novel contribution to tropical geometry.
Findings
Formula for the number of vertices based on degrees of hypersurfaces
Genus calculation for smooth, connected tropical curves
Enhanced understanding of tropical intersection theory
Abstract
A tropical complete intersection curve C in R^(n+1) is a transversal intersection of n smooth tropical hypersurfaces. We give a formula for the number of vertices of C given by the degrees of the tropical hypersurfaces. We also compute the genus of C (defined as the number of independent cycles of C) when C is smooth and connected.
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Taxonomy
TopicsPolynomial and algebraic computation · Algebraic Geometry and Number Theory · Advanced Numerical Analysis Techniques