FA-modules of holomorphic forms on $\overline{\mathcal{M}}_{g,n}$
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918138867613696 |
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| author | Canning, Samir Larson, Hannah Payne, Sam Willwacher, Thomas |
| author_facet | Canning, Samir Larson, Hannah Payne, Sam Willwacher, Thomas |
| contents | For fixed genus g and varying finite marking set A, the gluing and forgetful maps give the spaces of holomorphic forms on the moduli space of stable A-marked curves of genus g has the structure of an FA-module, i.e., a functor from the category of finite sets to vector spaces. We prove that the resulting FA-modules of holomorphic k-forms are simple, for k less than or equal to 18, whenever they are nonzero. Conditional upon the conjectured vanishing of holomorphic 19-forms and 20-forms in genus 3, for 15 and 16 marked points, respectively, this extends to k less than or equal to 20. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_08774 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | FA-modules of holomorphic forms on $\overline{\mathcal{M}}_{g,n}$ Canning, Samir Larson, Hannah Payne, Sam Willwacher, Thomas Algebraic Geometry 14H10, 14H15, 14J15, 18G85, 32G15 For fixed genus g and varying finite marking set A, the gluing and forgetful maps give the spaces of holomorphic forms on the moduli space of stable A-marked curves of genus g has the structure of an FA-module, i.e., a functor from the category of finite sets to vector spaces. We prove that the resulting FA-modules of holomorphic k-forms are simple, for k less than or equal to 18, whenever they are nonzero. Conditional upon the conjectured vanishing of holomorphic 19-forms and 20-forms in genus 3, for 15 and 16 marked points, respectively, this extends to k less than or equal to 20. |
| title | FA-modules of holomorphic forms on $\overline{\mathcal{M}}_{g,n}$ |
| topic | Algebraic Geometry 14H10, 14H15, 14J15, 18G85, 32G15 |
| url | https://arxiv.org/abs/2509.08774 |