Extended Torelli map to the Igusa blowup in genus 6, 7, and 8
Abstract
It was conjectured in NamikawaExtendedTorelli that the Torelli map Mg Ag associating to a curve its jacobian extends to a regular map from the Deligne-Mumford moduli space of stable curves Mg to the (normalization of the) Igusa blowup Ag cent. A counterexample in genus g=9 was found in AlexeevBrunyate. Here, we prove that the extended map is regular for all g8, thus completely solving the problem in every genus.
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