Algebraic hyperbolicity of surfaces in Fano threefolds with Picard number one

TL;DR

This paper investigates the algebraic hyperbolicity of very general surfaces within Fano threefolds of Picard number one, providing a complete classification except for weighted hypersurfaces.

Contribution

It offers a comprehensive classification of algebraic hyperbolicity for these surfaces, advancing understanding in the geometry of Fano threefolds.

Findings

Complete classification of algebraic hyperbolicity for surfaces in Fano threefolds

Identification of exceptions in weighted hypersurfaces

Enhanced understanding of surface geometry in Fano varieties

Abstract

In this paper, we study the algebraic hyperbolicity of very general surfaces in general Fano threefolds with Picard number one. We completely classify the algebraically hyperbolicity of those surfaces, except for surfaces in weighted hypersurfaces.