Kenta Hayano

Topology of holomorphic Lefschetz pencils on the four-torus

Although we can easily obtain holomorphic Lefschetz pencils by taking generic
pencils (i.e. linear 1-systems) of very ample line bundles, it is
difficult to get
vanishing cycles of such pencils.
In this talk, we will explain how to obtain vanishing cycles of holomorphic
Lefschetz pencils on the four-torus constructed via branched coverings,
and discuss
combinatorial properties of them.
If time permits, we will further discuss uniqueness of smooth isomorphism
classes of
holomorphic Lefschetz pencils on the four-torus.
This is joint work with Noriyuki Hamada (The University of Tokyo).