SEMINAR:On complex 4-nets30-11-2020

Speaker:  Ali Ulaş Özgür Kişisel,

Title:   On complex 4-nets

Date/Time: 2  December 2020/ 13:15- 14:15 

Zoom: Meeting ID  938 9328 8920

Passcode:  Algebra

Abstract:  Nets are certain special line arrangements in the plane and they occur in various contexts related to algebraic geometry, such as resonance varieties, homology of Milnor fibers and fundamental groups of curve complements. We will investigate nets in the complex projective plane $\mathbb{CP}^2$. Let $m\geq 3$ and $d\geq 2$ be integers. An $(m,d)$-net is a pencil of degree $d$ algebraic curves in $\mathbb{CP}^2$ with a base locus of exactly $d^2$ points, which degenerates into a union of $d$ lines $m$ times. It was conjectured that the only $4$-net is a $(4,3)$-net called the Hessian arrangement. I will outline our proof together with A. Bassa of this conjecture.

Bio:Ali Ulaş Özgür Kişisel received his bachelor's degree from Middle East Technical University in 1995 and his Ph.D. degree from University of California, Los Angeles in 2000. He has been a faculty member of the Middle East Technical University since 2000. His research areas include Algebraic Geometry, Number Theory, Combinatorics and Mathematical Physics.