Algebraic hyperbolicity of very general hypersurfaces in projective spaces

Source abstract

We prove that a very general sextic threefold in $\mathbb{P}^4$ is algebraically hyperbolic, settling the last open case and completing the classification of algebraic hyperbolicity for very general hypersurfaces in projective space. The proof follows the Coskun--Riedl scroll construction, with the moduli of stable maps and the logarithmic geometry of fibered surfaces as new ingredients.