Izzet Coskun, Eric Riedl. Algebraic Hyperbolicity of Very General Surfaces. Israel Journal of Mathematics. 2023.
Abstract
Recently, Haase and Ilten initiated the study of classifying algebraically hyperbolic surfaces in toric threefolds. We complete this classification for P1 \texttimes{} P1 \texttimes{} P1, P2 \texttimes{} P1, Fe \texttimes{} P1 and the blowup of P3 at a point, augmenting our earlier work on P3. In the process, we codify several different techniques for proving algebraic hyperbolicity, allowing us to prove similar results for hypersurface in any variety admitting a group action with dense orbit.