Examples of hyperbolic hypersurfaces of low degree in projective spaces

TL;DR

This paper constructs explicit examples of hyperbolic hypersurfaces with low degree in complex projective spaces of dimensions 3 to 6, advancing understanding of hyperbolic geometry in algebraic varieties.

Contribution

It provides new explicit constructions of hyperbolic hypersurfaces of degree 2n in projective spaces for dimensions 3 to 6, which were previously unknown.

Findings

Explicit families of hyperbolic hypersurfaces constructed

Degree of hypersurfaces is 2n in P^n for 3 ≤ n ≤ 6

Advances in hyperbolic geometry in algebraic varieties

Abstract

We construct families of hyperbolic hypersurfaces of degree $2n$ in the projective space $\mathbb{P}^n(\mathbb{C})$ for $3 \leq n \leq 6$.