Noriyuki Hamada

3/22(Tue.)(11:20-12:20)

Title

Various techniques of constructing Lefschetz pencils

Abstract

I will explain various techniques of constructing Lefschetz fibrations, especially pencils, mainly from the combinatorial viewpoint. By utilizing the chain number and the lantern number, which are combinatorial invariants of a monodromy factrizatio, we can make it easier to handle with the Euler characteristic and the signature of the pencil that we try to construct. Guessing those invariants in this way, we can construct new pencils by combining techniques such as substitution, partial conjugation, breeding, finite covering, and so on. In the talk, we will see explicit examples and observe that this strategy works well practically and effectively.