Regularity of the superstring supermeasure and the superperiod map

• Giovanni Felder ^[1] ; David Kazhdan ^[2] ; Alexander Polishchuk ^[3]
  1. [1] Swiss Federal Institute of Technology in Zurich

     Swiss Federal Institute of Technology in Zurich

     Zürich, Suiza

     
  2. [2] Hebrew University of Jerusalem

     Hebrew University of Jerusalem

     Israel

     
  3. [3] University of Oregon, USA; National Research University Higher School of Economics, Rusia; Korea Institute for Advanced Study, Corea del Sur

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 28, Nº. 1, 2022
• Idioma: inglés
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• Resumen

  • 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≤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.