On Stability of Nodal $L_k^p$-Maps I

TL;DR

This paper introduces a generalized stability concept for nodal $L_k^p$-maps, extending stability notions from $J$-holomorphic maps in Gromov-Witten theory, with a complete characterization based on isotropy groups.

Contribution

It provides a new definition of weakly stable nodal $L_k^p$-maps and characterizes their stability through isotropy groups, correcting previous errors.

Findings

Defines weakly stable nodal $L_k^p$-maps

Characterizes stability via isotropy groups

Corrects earlier inaccuracies in the theory

Abstract

We give a general definition of weakly stable nodal $L_k^p$-maps as a natural generalization of the stability for $J$-holomorphic nodal maps in GW theory. A complete characterization of the weakly stable nodal $L_k^p$-maps are given in term of their isotropy groups. Some errors in the earlier version are corrected