Tropical curves of unibranch points and hypertangency

Fuente: arXiv
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Main Authors: Caporaso, Lucia, Turchet, Amos
Format: Preprint
Published: 2024
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author Caporaso, Lucia
Turchet, Amos
author_facet Caporaso, Lucia
Turchet, Amos
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2406_17392
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Tropical curves of unibranch points and hypertangency
Caporaso, Lucia
Turchet, Amos
Algebraic Geometry
14H20, 14H50, 14T90
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.
title Tropical curves of unibranch points and hypertangency
topic Algebraic Geometry
14H20, 14H50, 14T90
url https://arxiv.org/abs/2406.17392