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 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. 
Valery Alexeev, Ryan Livingston, Joseph Tenini, Maxim Arap, Xiaoyan   Hu, Lauren Huckaba, Patrick Mcfaddin, Stacy Musgrave, ...
math.AG