Abstract
In the following three cases criteria are found for complements of divisors in compact complex manifolds to be hyperbolically embedded in the sense of Kobayashi: for divisors with normal crossings, for arbitrary divisors in complex surfaces, and for unions of hyperplanes in projective space. A criterion is given for two-dimensional polynomial polyhedra to be hyperbolically embedded, and Iitaka's conjecture about conditions for hyperbolicity of the complement of a set of projective lines is confirmed. Upper semicontinuity is proved for the Kobayashi-Royden pseudometrics and Kobayashi-Eisenman pseudovolumes of a family of complex manifolds containing degenerate fibers, and conditions are given under which the hyperbolic length (volume) on the smooth part of a degenerate fiber is the limit of the hyperbolic length (volume) on the nonsingular fibers.Bibliography: 28 titles.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
