Regularity of the superstring supermeasure and the superperiod map

Giovanni Felder; David Kazhdan; Alexander Polishchuk

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arXiv · 1905.12805

Regularity of the superstring supermeasure and the superperiod map

Giovanni Felder·David Kazhdan·Alexander Polishchuk

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Abstract

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.

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BibTeX RIS

Giovanni Felder, David Kazhdan, Alexander Polishchuk. 2019-05-30. Regularity of the superstring supermeasure and the superperiod map. https://arxiv.org/abs/1905.12805

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