Complex hyperbolicity from a pluripotential point of view

Speaker: Duc-Bao Nguyen，新加坡国立大学       

Inviter: 谢松晏

Title: Complex hyperbolicity from a pluripotential point of view

Language: English

Time & Venue: 2026.07.01  14:00-16:00   南楼N224

Abstract: In this talk, I will explain joint work with Tien-Cuong Dinh and Duc-Viet Vu, in which we revisit complex hyperbolicity using the theory of positive closed currents. More precisely, we introduce numerical invariants, called hyperbolic indices, which measure the hyperbolicity of a complex manifold. We prove that a complex manifold with positive hyperbolic indices is Kobayashi hyperbolic, and that a complex manifold with negative jet curvature has positive hyperbolic indices. In particular, by using the method of jet differentials and the theory of density currents, we show that the hyperbolic indices of a general hypersurface in projective space grow to infinity at least linearly as the degree tends to infinity.