Open Collections

Hyperbolicity for log pairs

Banff International Research Station for Mathematical Innovation and Discovery

A classical result in birational geometry, Mori’s Cone Theorem, implies that if the canonical bundle of a variety X is not nef then X contains rational curves. This is the starting point of the so-called Minimal Model Program. In particular, hyperbolic varieties are positive from the point of view of birational geometry. Very much in the same vein, one could ask what happens for a quasi projective variety, Y . Using resolution of singularity, then one is lead to consider pairs (X,D) of a variety and a divisor, such that Y = X \\ D. I will show how to obtain a theorem analogous to Mori’s Cone Theorem in this context. Instead of rational complete curves, algebraic copies of the complex plane will male their appearance. I will also discuss an ampleness criterion for hyperbolic pairs.\r\n

Mathematics; Several complex variables and analytic spaces; Algebraic geometry

video/mp4

Author affiliation: MIT

2016-05-05

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/58077

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/