Time：15:00-16:00, Thursday, January 8 2026
Venue: E14-416
Speaker：Kejia Zhu, Hunan University
Title：CAT(0) Geometry and residual finiteness of Complex Curve Complements and Families
Abstract：Motivated by the question of whether braid groups are CAT(0), we investigate the CAT(0) behavior of fundamental groups of plane curve complements and certain universal families. If C is the branch locus of a generic projection of a smooth, complete intersection surface to P^2 , we show that the fundamental group of P^2 ∖ C is CAT(0). In the other direction, we prove that the fundamental group of the universal family associated with the singularities of type E6, E7, and E8 is not CAT(0). We also show that when the degree of C is at most 5, the fundamental group of P^2 ∖ C is linear and virtually polyfree, as a consequence, we answer positively the question of Zariski on the residually finiteness of the fundamental group of P^2 ∖ C for all plane curves of degree at most 5.
This is joint work with C. Bregman, A. Libgober, and Shengkui Ye.
