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A measure on the moduli space of super Riemann surfaces with Ramond punctures

Ron Donagi, Nadia Ott

Abstract

We construct a measure on the moduli space of super Riemann surfaces with Ramond punctures using the super Mumford isomorphism and a super period map.

A measure on the moduli space of super Riemann surfaces with Ramond punctures

Abstract

We construct a measure on the moduli space of super Riemann surfaces with Ramond punctures using the super Mumford isomorphism and a super period map.

Paper Structure

This paper contains 29 sections, 10 theorems, 100 equations.

Table of Contents

  1. Introduction
  2. Super Riemann surfaces and their moduli
  3. Mumford isomorphisms
  4. The pairing
  5. The measure
  6. Further comments
  7. Preliminaries: Super Riemann surfaces with Ramond punctures
  8. Correspondence with twisted spin curves.
  9. Families of super Riemann surfaces with Ramond punctures
  10. Superconformal Coordinates.
  11. Change of superconformal coordinates and orientation on the Ramond Divisor.
  12. Periods of super Riemann surfaces with Ramond punctures
  13. Extended Berezinian sheaf
  14. Periods of super Riemann surfaces with Ramond punctures
  15. Odd Period Map.
  16. ...and 14 more sections

Key Result

Lemma 2.2

Let $\pi: X \to T$ be a family of super Riemann surfaces with Ramond divisor $R$, and let $\mathcal{Z}_{R/T}^1$ denote the sheaf of relative closed one-forms on $R$. Its pushforward $\pi_* \mathcal{Z}_{R/T}^1$ is a vector bundle of rank $0|2r$ on $T$ associated to a local system $\Lambda_1$ of free

Theorems & Definitions (22)

  • Remark 1.1
  • Definition 2.1
  • Lemma 2.2
  • proof
  • Lemma 4.1
  • proof
  • Theorem 4.2
  • proof
  • Theorem 5.1
  • proof
  • ...and 12 more