Multiscale differentials and wonderful models
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917986365865984 |
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| author | Devkota, Prabhat Robotis, Antonios-Alexandros Zahariuc, Adrian |
| author_facet | Devkota, Prabhat Robotis, Antonios-Alexandros Zahariuc, Adrian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_11534 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multiscale differentials and wonderful models Devkota, Prabhat Robotis, Antonios-Alexandros Zahariuc, Adrian Algebraic Geometry Complex Variables 14H10, 14M27, 30F30 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. |
| title | Multiscale differentials and wonderful models |
| topic | Algebraic Geometry Complex Variables 14H10, 14M27, 30F30 |
| url | https://arxiv.org/abs/2504.11534 |