Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.

2015 (English)In: Duke mathematical journal, ISSN 0012-7094, E-ISSN 1547-7398, Vol. 164, no 2, p. 195-233Article in journal (Refereed) Published

Abstract [en]

We prove the existence of extremal, nonconstant-scalar curvature, Kahler metrics on certain unstable projectivized vector bundles P(E) -> M over a compact constant scalar curvature Kahler manifold M with discrete holomorphic automorphism group, in certain adiabatic Kahler classes. In particular, the vector bundles E -> M are assumed to split as a direct sum of stable subbundles E = El circle plus ... circle plus E-s all having different Mumford-Takemoto slope, for example, mu(E-1) > ... > mu(E-s).