Strict and nonstrict positivity of direct image bundles

• 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.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

manifolds

space

manifolds

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