K-nets over a field

Fernando Figueroa Zamora, Princeton University
Fine Hall 110

A k-net is a finite collection of lines divided into k disjoint subsets (called components), such that through each intersection of two lines from different components passes exactly one line from each component. Over the complex numbers only one 4-net is known and is conjectured to be the only possibile case. In general the problem of classifying k-nets over a field can be quite difficult. In this talk we will study some properties of line arrangements embedded in the projective plane and show an elementary proof of the non-existence of 5-nets over fields of characteristic zero.