Geometry Topology Seminar : Surface bundles and complex projective varieties by Corey Bregman

Geometry Topology Seminar
Monday, September 30, 2019 - 2:00pm for 1 hour (actually 50 minutes)
Skiles 006
Corey Bregman – Brandeis University – cbregman@brandeis.edu
JungHwan Park

Kodaira, and independently Atiyah, gave the first examples of surface bundles over surfaces whose signature does not vanish, demonstrating that signature need not be multiplicative.  These examples, called Kodaira fibrations, are in fact complex projective surfaces admitting a holomorphic submersion onto a complex curve, whose fibers have nonconstant moduli. After reviewing the Atiyah-Kodaira construction, we consider Kodaira fibrations with nontrivial holomorphic invariants in degree one. When the dimension of the invariants is at most two, we show that the total space admits a branched covering over a product of curves.