The Lefschetz condition on projectivizations of complex vector bundles
Commun. Korean Math. Soc. 2014 Vol. 29, No. 4, 569-579
Printed October 1, 2014
Hirokazu Nishinobu and Toshihiro Yamaguchi
Kochi University, Kochi University
Abstract : 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
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