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arXiv · 2509.08774

FA-modules of holomorphic forms on $\overline{\mathcal{M}}_{g,n}$

Samir Canning·Hannah Larson·Sam Payne·Thomas Willwacher
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Abstract

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.

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Samir Canning, Hannah Larson, Sam Payne, Thomas Willwacher. 2025-09-10. FA-modules of holomorphic forms on $\overline{\mathcal{M}}_{g,n}$. https://arxiv.org/abs/2509.08774

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