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

Abstract

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 ${\bar{A}}_g^{\mathrm{cent}}$. A counterexample in genus $g=9$ was found in \cite{AlexeevBrunyate}. Here, we prove that the extended map is regular for all $g\le 8$, thus completely solving the problem in every genus.

To appear in Experimental Mathematics