Construction of hyperbolic hypersurfaces of low degree in $\mathbb{p}^n(\mathbb{c})$

TL;DR

This paper constructs specific families of hyperbolic hypersurfaces in complex projective space with degrees above a certain threshold, advancing understanding of their geometric properties.

Contribution

It introduces new constructions of hyperbolic hypersurfaces of low degree in complex projective spaces, expanding the known examples in complex geometry.

Findings

Constructed hyperbolic hypersurfaces of degree d ≥ ((n+3)/2)^2

Established existence of such hypersurfaces in complex projective space

Provided explicit families of hyperbolic hypersurfaces

Abstract

We construct families of hyperbolic hypersurfaces $X_d\subset\mathbb{P}^{n+1}(\mathbb{C})$ of degree $d\geq {\textstyle{(\frac{n+3}{2})^2}}$.