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Weakly K\"ahler hyperbolic manifolds and the Green--Griffiths--Lang conjecture by Bei, Francesco; Diverio, Simone; Eyssidieux, Philippe; Trapani, Stefano is a scholarly article available to read on EtoBox.

What is Weakly K\"ahler hyperbolic manifolds and the Green--Griffiths--Lang conjecture about?

We introduce the notion of weakly K\"ahler hyperbolic manifold which generalizes that of K\"ahler hyperbolic manifold given in the early '90s by M. Gromov, and establish its basic features. We then investigate its spectral properties and show a spectral gap result (on a suitable modification). As applications, we prove that weakly K\"ahler hyperbolic manifolds are of general type and we study the geometry of their subvarieties and entire curves, verifying -- among other things -- various aspects of the Lang and the Green--Griffiths conjectures for this class of manifolds.

Author

Bei, Francesco; Diverio, Simone; Eyssidieux, Philippe; Trapani, Stefano

Published

2022

Language

EN