Algebraic hyperbolicity of very general hypersurfaces in weighted projective spaces

TL;DR

This paper establishes bounds on the degree of hypersurfaces in weighted projective spaces that ensure they are algebraically hyperbolic, contributing to the understanding of hyperbolicity in algebraic geometry.

Contribution

It introduces new bounds for algebraic hyperbolicity of very general hypersurfaces in weighted projective spaces, extending previous results to singular ambient spaces.

Findings

Bound for $m$ ensuring algebraic hyperbolicity

Applicable to hypersurfaces in weighted projective spaces with isolated singularities

Generalization of hyperbolicity criteria to weighted settings

Abstract

We provide a bound for $m$ such that the zero locus of a very general section of an $m$-multiple of some ample line bundle on a weighted projective space with isolated singularities is algebraically hyperbolic.