# On Action of $PSL(n+1, {\bf C})$ on Space of $L_k^p$-maps on ${\bf P}^n$

## TL;DR

This paper proves the properness of the action of the projective special linear group on the space of certain stable maps on complex projective space, advancing understanding of symmetries in geometric analysis.

## Contribution

It establishes the properness of the group action on the space of $L_k^p$-maps, providing new insights into the structure of these moduli spaces.

## Key findings

- Properness of the $PSL(n+1, f C)$ action on $L_k^p$-maps
- Results on $v$-stability of maps
- Implications for geometric analysis and moduli space structure

## Abstract

In this paper, we prove properness of the action of the reparametrization group $PSL(n+1, {\bf C})$ on the space of $v$-stable $L_k^p$-maps on ${\bf P}^n$ as well as related results.