Knets over a field
Knets over a field

Fernando Figueroa Zamora, Princeton University
Fine Hall 110
A knet 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 4net is known and is conjectured to be the only possibile case. In general the problem of classifying knets 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 nonexistence of 5nets over fields of characteristic zero.