THE LEFSCHETZ CONDITION ON PROJECTIVIZATIONS OF COMPLEX VECTOR BUNDLES

Abstract

We consider a condition under which the projectivization <TEX>$P(E^k)$</TEX> of a complex k-bundle <TEX>$E^k{\rightarrow}M$</TEX> over an even-dimensional manifold M can have the hard Lefschetz property, affected by [10]. It depends strongly on the rank k of the bundle <TEX>$E^k$</TEX>. Our approach is purely algebraic by using rational Sullivan minimal models [5]. We will give some examples.