Strict and nonstrict positivity of direct image bundles

Berndtsson, Bo, 1950 (author): Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper, matematik,Department of Mathematical Sciences, Mathematics,University of Gothenburg,Chalmers tekniska högskola,Chalmers University of Technology

(creator_code:org_t)

2010-10-06
2011
English.
In: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 0025-5874 .- 1432-1823. ; 269:3-4, s. 1201-1218

Related links:: http://arxiv.org/pdf...; show more...; http://dx.doi.org/10...; https://gup.ub.gu.se...; https://doi.org/10.1...; https://research.cha...; show less...

Abstract Subject headings

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.

About the subject

By the university: University of Gothenburg; Chalmers University of Technology

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