Communications of the
Korean Mathematical Society CKMS

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

Keywords: projectivization, c-symplectic, the Lefschetz property, Sullivan model, formal, projective (n)-Lefschetz, projective non-Lefschetz

MSC numbers: 55P62, 57R17