Applications of a grassmannian technique in hypersurfaces

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.

References in corpus (3)

• Effectivity in the Hyperbolicity-related problems
• Rational curves on general type hypersurfaces
• Rationally Equivalent Points On Hypersurfaces In ${\mathbb{P}}^n$

Cited by in corpus (3)

• Degrees $d⩾(\sqrt{n}\log n{)}^n$ and $d⩾(n\log n{)}^n$ in the Conjectures of Green-Griffiths and of Kobayashi
• Rationally Equivalent Points On Hypersurfaces In ${\mathbb{P}}^n$
• Effective bounds on ampleness of cotangent bundles