Strict and nonstrict positivity of direct image bundles
Journal article, 2011

This paper is a sequel to (Berndtsson in Ann Math 169:531-560, 2009). In that paper we studied the vector bundle associated to the direct image of the relative canonical bundle of a smooth Kahler morphism, twisted with a semipositive line bundle. We proved that the curvature of a such vector bundles is always semipositive (in the sense of Nakano). Here we address the question if the curvature is strictly positive when the Kodaira-Spencer class does not vanish. We prove that this is so provided the twisting line bundle is strictly positive along fibers, but not in general.

manifolds

space

Author

Bo Berndtsson

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Mathematische Zeitschrift

0025-5874 (ISSN) 1432-8232 (eISSN)

Vol. 269 3-4 1201-1218

Subject Categories

Mathematics

DOI

10.1007/s00209-010-0783-5

More information

Created

10/7/2017