Regularity of the superstring supermeasure and the superperiod map

Understand

The supermeasure whose integral is the genus $g$ vacuum amplitude of superstring theory is potentially singular on the locus in the moduli space of supercurves where the corresponding even theta-characteristic has nontrivial sections.

• We show that the supermeasure is actually regular for $g\leq 11$.
• The result relies on the study of the superperiod map.
• We also show that the minimal power of the classical Schottky ideal that annihilates the image of the superperiod map is equal to $g$ if $g$ is odd and is equal to $g$ or $g-1$ if $g$ is even.