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arXiv · 2508.16323

Curves on surfaces with prescribed pairwise intersection numbers

Ferit Öztürk
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Abstract

Given an ordered sequence of $N$-choose-2 integers, we give necessary and sufficient conditions to have an ordered collection of $N$ simple closed curves on a torus such that the algebraic pairwise intersections of those curves are the given integers. We also present partial answers towards realizing curve systems on a surface with minimal genus, given the intersection numbers.

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Ferit Öztürk. 2025-08-22. Curves on surfaces with prescribed pairwise intersection numbers. https://arxiv.org/abs/2508.16323

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