Lefschetz Defect in Families

Abstract

We provide a cohomological characterization of the Lefschetz defect of smooth complex projective varieties. As a consequence, we deduce that the Lefschetz defect of a smooth Fano variety is invariant under smooth deformation. We also characterize the Lefschetz defect of an abelian variety in terms of its isogeny factors, and study it in families.

16 pages, published in Manuscripta Mathematica. Fixed a mistake in the main theorem, found by an anonymous referee (Remark 2.6), by improving the results of Subsection 3.2. Last subsection on families of abelian varieties from previous version has been removed