Effectivity in the Hyperbolicity-related problems

Ya Deng (1)

1 IF - Institut Fourier

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.

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 Hyperbolicity-related problems. 2016. ⟨hal-01308628v4⟩