On the stability of foliations of degree 3 with a unique singular point

2023/04/10 by Castorena, Abel, Pantaleón-Mondragón, P. Rubí, Aquino, Juan Vásquez
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2304.04352

Abstract

Applying Geometric Invariant Theory (GIT), we study the stability of foliations of degree 3 on P² 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.

Related

• Invariant theory of foliations of the projective plane
• Foliations on ℙ² with only one singular point
• Remarks on foliations on \mathbbCP² with a unique singular point
• Stability of branched pull-back projective foliations
• Foliations on Projective Complete Intersection K3 Surfaces