Algebraic hyperbolicity of very general hypersurfaces in homogeneous varieties

TL;DR

This paper extends existing methods to establish near-optimal degree bounds for algebraic hyperbolicity of very general hypersurfaces in rational homogeneous varieties, including Grassmannians and flag varieties.

Contribution

It generalizes techniques to derive bounds on hypersurface degrees ensuring algebraic hyperbolicity in a broad class of homogeneous varieties.

Findings

Derived almost optimal degree bounds for hyperbolicity.

Applied results to Grassmannians and flag varieties.

Extended techniques to new classes of homogeneous varieties.

Abstract

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 rational homogeneous varieties. As examples, we work out the cases of very general hypersurfaces in Grassmannians and products therefore, orthogonal and symplectic Grassmannians, and flag varieties.