Intersecting a curve in an abelian variety with multiples of another curve

Fabrizio Barroero; Gabriel A. Dill; Lars Kuehne

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arXiv · 2610.10212

Intersecting a curve in an abelian variety with multiples of another curve

Fabrizio Barroero·Gabriel A. Dill·Lars Kuehne

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Abstract

Levin asked what can be said about the locus of points lying on a given curve in $\mathbb{G}_m^n$ that have a non-zero integer multiple on another given curve in $\mathbb{G}_m^n$ for $n \geq 3$. We give a definite answer to the abelian analogue of Levin's question, proving what is predicted by the Zilber--Pink conjecture in this case. An important ingredient in our proof is a strengthening of a height inequality by Vojta and Rémond.

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BibTeX RIS

Fabrizio Barroero, Gabriel A. Dill, Lars Kuehne. 2026-10-07. Intersecting a curve in an abelian variety with multiples of another curve. https://arxiv.org/abs/2610.10212

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