推广的Torelli映射到亏格6，7，8的Igusa爆破
Extended Torelli map to the Igusa blowup in genus 6, 7, and 8
摘要：
在\cite{Namikawa_ExtendedTorelli}中证明了与曲线的雅可比矩阵相关联的Torelli映射$M_g\to A_g$扩展到从稳定曲线的Deligne-Mumford模空间$\bar{M}_g$到Igusa blowup $\bar{A}_g^{\rm cent}$（的归一化）的正则映射。在\cite{AlexeevBrunyate}中发现了一个$g=9$属的反例。在这里，我们证明了扩展映射是正则的所有$g\le8$，从而完全解决了在每个属的问题。
英文摘要：
It was conjectured in \cite{Namikawa_ExtendedTorelli} that the Torelli map $M_g\to A_g$ associating to a curve its jacobian extends to a regular map from the Deligne-Mumford moduli space of stable curves $\bar{M}_g$ to the (normalization of the) Igusa blowup $\bar{A}_g^{\rm cent}$. A counterexample in genus $g=9$ was found in \cite{AlexeevBrunyate}. Here, we prove that the extended map is regular for all $g\le8$, thus completely solving the problem in every genus.
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