We generalize techniques by Coskun, Riedl, and Yeong, and obtain an almost optimal bound on the degree for the algebraic hyperbolicity of very general hypersurfaces in homogeneous varieties. As examples, we work out the cases of very general hypersurfaces in products of Grassmannians, orthogonal and symplectic Grassmannians, and flag varieties.PDF: Algebraic hyperbolicity of very general hypersurfaces in homogeneous varieties.pdf
