Applications of a grassmannian technique in hypersurfaces

2018/06/06 by Riedl, Eric, Yang, David
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1806.02364

Abstract

In this paper we further develop a Grassmannian technique used to prove results about very general hypersurfaces and present three applications. First, we provide a short proof of the Kobayashi Conjecture given previous results on the Green-Griffiths-Lang Conjecture. Second, we characterize the dimension of the space of Chow-equivalent points on a very general hypersurface, proving the remaining cases of a conjecture of Chen, Lewis and Sheng and providing a short, alternate proof for many of the already known cases. Finally, we relate Seshadri constants of very general points to Seshadri constants of arbitrary points of very general hypersurfaces.

Related

• Proof of the Kobayashi conjecture on the hyperbolicity of very general hypersurfaces
• Algebraic hyperbolicity of very general hypersurfaces in homogeneous varieties
• Non-reductive geometric invariant theory and hyperbolicity
• Degrees d \geqslant ( √(n) log n)ⁿ and d \geqslant ( n log n)ⁿ in the Conjectures of Green-Griffiths and of Kobayashi
• Special points on intersections of hypersurfaces