发表机构
Peking University（北京大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究稳定带标曲线模空间间忘却映射的分解定理，证明当m趋于无穷时，$\bar{\textit{M}}_{g,n}$的每个层闭包为分解定理的直和项支集，证明用到Hassett的模空间及跨壁论证。
AI 中文摘要
本文研究亏格为g的稳定带标曲线模空间之间忘却映射$\boldsymbol{\bar{\boldsymbol{\textit{M}}}}_{\boldsymbol{g,m}}\to \boldsymbol{\bar{\boldsymbol{\textit{M}}}}_{\boldsymbol{g,n}}$的分解定理。我们证明当m趋于无穷时，$\boldsymbol{\bar{\boldsymbol{\textit{M}}}}_{\boldsymbol{g,n}}$中的每个层闭包都会作为分解定理中一个直和项的支集出现，证明用到了Hassett的稳定加权带标曲线模空间及跨壁论证。
英文摘要
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.
Comments15 pages; v2: included an effective bound. Comments welcome!
