# THE LEFSCHETZ CONDITION ON PROJECTIVIZATIONS OF COMPLEX VECTOR BUNDLES

Nishinobu, Hirokazu;Yamaguchi, Toshihiro

• Published : 2014.10.31
• 30 6

#### Abstract

We consider a condition under which the projectivization $P(E^k)$ of a complex k-bundle $E^k{\rightarrow}M$ 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 $E^k$. Our approach is purely algebraic by using rational Sullivan minimal models [5]. We will give some examples.

#### Keywords

projectivization;c-symplectic;the Lefschetz property;Sullivan model;formal;projective (n)-Lefschetz;projective non-Lefschetz

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