New examples of hyperbolic octic surfaces in $\PP^3$

TL;DR

This paper demonstrates that small deformations of the union of two cones in projective three-space produce new examples of hyperbolic surfaces, expanding the known classes of such surfaces for degrees eight and above.

Contribution

It introduces a novel method of constructing hyperbolic surfaces in P3 through deformations of cone unions, providing new explicit examples for degrees d >= 8.

Findings

Small deformations of cone unions yield hyperbolic surfaces.

New hyperbolic surfaces constructed for degrees d >= 8.

Method extends known examples of hyperbolic surfaces.

Abstract

We show that a general small deformation of the union of two general cones in P3 of degree >= 4 is Kobayashi hyperbolic. Hence we obtain new examples of hyperbolic surfaces in P3 of any given degree d>= 8.