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arXiv · 2504.11534

Multiscale differentials and wonderful models

Prabhat Devkota·Antonios-Alexandros Robotis·Adrian Zahariuc
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Abstract

We study the relationships between several varieties parametrizing marked curves with differentials in the literature. More precisely, we prove that the space $\mathcal{B}_n$ of multiscale differentials of genus 0 with $n+1$ marked points of orders $(0,\ldots,0,-2)$ is a wonderful variety. This shows that the Chow ring of $\mathcal{B}_n$ is generated by the classes of a collection of smooth boundary divisors with normal crossings subject to simple and explicit linear and quadratic relations. Furthermore, we realize $\mathcal{B}_n$ as a subvariety of the space $\mathcal{A}_n$ of multiscale lines and prove that $\mathcal{B}_n$ can be realized as the normalized Chow quotient of $\mathcal{A}_n$ by a natural $\mathbb{C}^*$-action.

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Prabhat Devkota, Antonios-Alexandros Robotis, Adrian Zahariuc. 2025-04-15. Multiscale differentials and wonderful models. https://arxiv.org/abs/2504.11534

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