2 research outputs found
The Euler-Betti Algorithm to identify foliations in Hilbert Scheme
Foliations in the complex projective plane are uniquely determined by their
singular locus, which is in correspondence with a zero-dimensional ideal.
However, this correspondence is not surjective. We give conditions to determine
whether an ideal arises as the singular locus of a foliation or not.
Furthermore, we give an effective method to construct the foliation in the
positive case
On the stability of foliations of degree 3 with a unique singular point
Applying Geometric Invariant Theory (GIT), we study the stability of
foliations of degree 3 on 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