# Properties of the moduli set of complete connected projective special real manifolds

## TL;DR

This paper constructs a convex set representing the moduli space of certain geometric manifolds and characterizes regular boundary behavior, with applications to deformations in supergravity theories.

## Contribution

It introduces a compact convex set for the moduli of projective special real manifolds and characterizes their boundary behavior, advancing understanding of their deformation theory.

## Key findings

- Constructed a convex generating set $\
- $ of the moduli space.
- Characterized when a manifold has regular boundary behavior.

## Abstract

We construct a compact convex generating set $\mathcal{C}_n$ of the moduli set of closed connected projective special real manifolds of fixed dimension $n$. We show that a closed connected projective special real manifold corresponds to an inner point of $\mathcal{C}_n$ if and only if it has regular boundary behaviour. Our results can be used to describe deformations of 5d supergravity theories with complete scalar geometries.