What question did this study set out to answer?

The aim is to establish almost optimal bounds on the degree for algebraic hyperbolicity of hypersurfaces in homogeneous varieties.

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March 21, 2026Open Access

Algebraic hyperbolicity of very general hypersurfaces in homogeneous varieties

Key Points

The aim is to establish almost optimal bounds on the degree for algebraic hyperbolicity of hypersurfaces in homogeneous varieties.
Generalized existing techniques from previous research
Analyzed specific cases such as Grassmannians and flag varieties
Considered orthogonal and symplectic Grassmannians.
Obtained almost optimal bounds for algebraic hyperbolicity
Detailed cases for very general hypersurfaces in identified 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.

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