Abstract
It was conjectured in Yukihiko Namikawa, “On the Canonical Holomorphic Map from the Moduli Space of Stable Curves to the Igusa Monoidal Transform,” 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 $\bar{A}^{\rm cent}_g$. A counterexample in genus $g = 9$ was found in Valery Alexeev and Adrian Brunyate, “Extending Torelli Map to Toroidal Compactifications of Siegel Space.” Here, we prove that the extended map is regular for all $g \le 8$, thus completely solving the problem in every genus.
Citation
Valery Alexeev. Catherine Ulrich. Ryan Livingston. Joseph Tenini. Maxim Arap. Xiaoyan Hu. Lauren Huckaba. Patrick McFaddin. Stacy Musgrave. Jaeho Shin. "Extended Torelli Map to the Igusa Blowup in Genus 6, 7, and 8." Experiment. Math. 21 (2) 193 - 203, 2012.
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