TY - JOUR
T1 - Regularity of the superstring supermeasure and the superperiod map
AU - Felder, Giovanni
AU - Kazhdan, David
AU - Polishchuk, Alexander
N1 - Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
PY - 2022/2
Y1 - 2022/2
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85121128488&partnerID=8YFLogxK
U2 - 10.1007/s00029-021-00727-1
DO - 10.1007/s00029-021-00727-1
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AN - SCOPUS:85121128488
SN - 1022-1824
VL - 28
JO - Selecta Mathematica, New Series
JF - Selecta Mathematica, New Series
IS - 1
M1 - 17
ER -