The bad locus in the moduli of super Riemann surfaces with Ramond punctures

TL;DR

This paper investigates the bad locus in the moduli space of super Riemann surfaces with Ramond punctures, showing it as the intersection of divisors where super period maps blow up, and provides bounds on its dimension.

Contribution

It identifies the bad locus as the intersection of blowup divisors in the super period map, using linear algebra to analyze its structure and bounds.

Findings

The bad locus corresponds to the intersection of divisors where period maps blow up.

At least one period map remains finite outside the bad locus.

Bounds on the dimension of the bad locus are established.

Abstract

The bad locus in the moduli of super Riemann surfaces with Ramond punctures parametrizes those super Riemann surfaces that have more than the expected number of independent closed holomorphic 1-forms. There is a super period map that depends on certain discrete choices. For each such choice, the period map blows up along a divisor that contains the bad locus. Our main result is that away from the bad locus, at least one of these period maps remains finite. In other words, we identify the bad locus as the intersection of the blowup divisors. The proof abstracts the situation into a question in linear algebra, which we then solve. We also give some bounds on the dimension of the bad locus.