# Regularity of the superstring supermeasure and the superperiod map

@article{Felder2021RegularityOT, title={Regularity of the superstring supermeasure and the superperiod map}, author={Giovanni Felder and David Kazhdan and Alexander Polishchuk}, journal={Selecta Mathematica}, year={2021} }

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…

## 8 Citations

Moduli and periods of supersymmetric curves

- MathematicsAdvances in Theoretical and Mathematical Physics
- 2019

Supersymmetric curves are the analogue of Riemann surfaces in super geometry. We establish some foundational results about complex Deligne-Mumford superstacks, and we then prove that the moduli…

The supermoduli space of genus zero SUSY curves with Ramond punctures

- Mathematics
- 2019

We give an explicit construction of the supermoduli space $\mathfrak{M}_{0, n_R}$ of super Riemann surfaces (SUSY curves) of genus zero with $n_R \ge 4$ Ramond punctures as a quotient Deligne-Mumford…

The supermoduli of SUSY curves with Ramond punctures

- Mathematics
- 2019

We construct local and global moduli spaces of supersymmetric curves with Ramond-Ramond punctures. We assume that the underlying ordinary algebraic curves have a level n structure and build these…

Super $$J$$-holomorphic curves: construction of the moduli space

- MathematicsMathematische Annalen
- 2021

Let $M$ be a super Riemann surface with holomorphic distribution $\mathcal{D}$ and $N$ a symplectic manifold with compatible almost complex structure $J$. We call a map $\Phi\colon M\to N$ a super…

Notes on fundamental algebraic supergeometry. Hilbert and Picard superschemes.

- Mathematics
- 2020

These notes aim at providing a complete and systematic account of some foundational aspects of algebraic supergeometry, namely, the extension to the geometry of superschemes of many classical…

Enumerative geometry via the moduli space of super Riemann surfaces

- Mathematics
- 2020

In this paper we relate volumes of moduli spaces of super Riemann surfaces to integrals over the moduli space of stable Riemann surfaces $\overline{\cal M}_{g,n}$. This allows us to use a recursion…

The moduli space of stable supercurves and its canonical line bundle

- Mathematics
- 2020

We prove that the moduli of stable supercurves with punctures is a smooth proper DM stack and study an analog of the Mumford's isomorphism for its canonical line bundle.

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