Effectivity in the Hyperbolicity-related problems

Abstract

The aim of this work is to deal with effective questions related to the Kobayashi and Debarre conjectures, and based on the work of Damian Brotbek and Lionel Darondeau. We first show that if a line bundle $L$ generates $k$-jets, the $k$-th Wronskian ideal sheaf associated with global sections of $L$ reaches its largest possible value. Then we obtain an effective estimate for a weaker version of a theorem of Nakamaye on certain universal Grassmannians. We finally derive from this explicit effective bounds for the Kobayashi and Debarre conjectures.

References in corpus (3)

• Proof of the Kobayashi conjecture on the hyperbolicity of very general hypersurfaces
• On the ampleness of the cotangent bundles of complete intersections
• Generalized Brotbek's symmetric differential forms and applications

Cited by in corpus (8)

• Applications of a grassmannian technique in hypersurfaces
• Nakamaye's theorem on complex manifolds
• On the Diverio-Trapani Conjecture
• Degrees $d⩾(\sqrt{n}\log n{)}^n$ and $d⩾(n\log n{)}^n$ in the Conjectures of Green-Griffiths and of Kobayashi
• Hyperbolicity of cyclic covers and complements
• A remark on the intersection of plane curves
• Effective bounds on ampleness of cotangent bundles
• On the positivity of the logarithmic cotangent bundle