Dear Colleagues,
 

You are most cordially invited to the seminar organized by the Department of Mathematics.

Title: On complex 4-nets 

Speaker: Ali Ulaş Özgür Kişisel (Middle East Technical University)

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.

Note: You may obtain a pdf copy of the abstract from here.