On the GIT-Stability of Foliations of Degree 3 with a Unique Singular Point

Abstract

Applying Geometric Invariant Theory (GIT), we study the stability of foliations of degree 3 on $$\mathbb {P}^{2}$$ P 2 with a unique singular point of multiplicity 1, 2, or 3 and Milnor number 13. In particular, we characterize those foliations for multiplicity 2 in three cases: stable, strictly semistable, and unstable.