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

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

2011-05-23

arxiv.org/abs/1105.4384v2

Mathematics

Algebraic Geometry

To appear in Experimental Mathematics

Scientific paper

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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