Analysis of the weight Diagram Associated with Foliations on the $\mathbb{CP}^{2}$

TL;DR

This paper examines the weight diagram of foliations on the complex projective plane using Geometric Invariant Theory, emphasizing invariants like algebraic multiplicity and invariant curves.

Contribution

It applies the Hilbert-Mumford criterion to analyze the weight diagram of foliations, highlighting key invariants and their geometric implications.

Findings

Identifies the structure of weight diagrams for foliations on ^2

Links invariants such as algebraic multiplicity to geometric properties

Provides criteria for the existence of invariant curves

Abstract

We analyze the weight diagram associated with foliations on the complex projective plane through the Hilbert-Mumford criterion in Geometric Invariant Theory, focusing in particular on invariants such as the algebraic multiplicity and the existence of invariant curves.