Abstract:
We will discuss results on the Lefschetz standard
conjecture for degree 2 cohomology of hyper-Kaehler manifolds
admitting a covering by Lagrangian subvarieties. In the case of a
Lagrangian fibration, we show that the Lefschetz standard conjecture
is implied by the SYZ conjecture characterizing classes of divisors
associated with Lagrangian fibrations. In the more general case of a
Lagrangian covering, we give a numerical criterion implying the
Lefschetz standard conjecture in degree 2. We will also discuss
potential applications to the study of the Chow ring and the group
of 0-cycles.
