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arXiv · 2608.10461

A Murphy's law for supports of forgetful maps between moduli spaces of stable pointed curves

Hao Zhang
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Abstract

We study in this note the decomposition theorem for forgetful maps between moduli spaces of genus $g$ stable pointed curves $\overline{\mathcal{M}}_{g,m}\to \overline{\mathcal{M}}_{g,n}$. We prove that as $m$ goes to infinity, every stratum closure in $\overline{\mathcal{M}}_{g,n}$ appears as the support of a direct summand in the decomposition theorem. The proof uses Hassett's moduli spaces of stable weighted pointed curves and a wall-crossing argument.

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Hao Zhang. 2026-09-16. A Murphy's law for supports of forgetful maps between moduli spaces of stable pointed curves. https://arxiv.org/abs/2608.10461

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