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arXiv · 2406.17392

Tropical curves of unibranch points and hypertangency

Lucia Caporaso·Amos Turchet
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Abstract

We study integral plane curves meeting at a single unibranch point and show that such curves must satisfy two equivalent conditions. A numeric condition: the local invariants of the curves at the contact point must be arithmetically related. A geometric condition: the tropical curves that we associate to the contact point must be isomorphic. Moreover, we prove closed formulas for the delta-invariant of a unibranch singularity, and for the dimension of the loci of curves with an assigned unibranch point. Our work is motivated by interest in the Lang exceptional set.

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Lucia Caporaso, Amos Turchet. 2024-06-25. Tropical curves of unibranch points and hypertangency. https://arxiv.org/abs/2406.17392

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