Extended Torelli map to the Igusa blowup in genus 6, 7, and 8

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 counterex...

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Bibliographic Details
Published in:arXiv.org 2011-10
Main Authors: Alexeev, Valery, Livingston, Ryan, Tenini, Joseph, Arap, Maxim, Hu, Xiaoyan, Huckaba, Lauren, Mcfaddin, Patrick, Musgrave, Stacy, Shin, Jaeho, Ulrich, Catherine
Format: Article
Language:English
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Summary: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.
ISSN:2331-8422