Poincar\'e problem for weighted projective foliations

TL;DR

This paper establishes bounds on the degree of quasi-smooth hypersurfaces in weighted projective spaces that are invariant under one-dimensional holomorphic foliations, advancing understanding of foliation invariants in complex geometry.

Contribution

It provides new degree bounds for invariant hypersurfaces in weighted projective spaces under holomorphic foliations, extending classical results to weighted settings.

Findings

Derived explicit degree bounds for invariant hypersurfaces.

Extended classical foliation invariance results to weighted projective spaces.

Enhanced understanding of the interaction between foliations and hypersurface degrees.

Abstract

We give a bounding of degree of quasi-smooth hypersurfaces which are invariant by a one dimensional holomorphic foliation of a given degree on a weighted projective space.