Effectivity in the Kobayashi and Debarre Conjectures

Ya Deng (1)

1 IF - Institut Fourier

The aim of this work is to deal with effective problems in the Kobayashi and Debarre conjectures, based on the work by Damian Brotbek and Lionel Darondeau. We first show that if the line bundle $L$ separates $k$-jets, the $k$-th Wronskian ideal sheaf for $L$ is stable. Then we obtain an effective estimate in the ``almost" Nakamaye Theorem for the universal Grassmannian. Finally we get explicit effective bounds for the Kobayashi and Debarre conjectures.

Mots clés: Kobayashi hyperbolic; Effective bounds; Nakamaye Theorem; Wronskian; Demailly-Semple tower; Universal Grassmannian

Domaines: Géométrie algébrique [math.AG]; Variables complexes [math.CV]

Ya Deng. Effectivity in the Kobayashi and Debarre Conjectures. 2016. ⟨hal-01308628v2⟩