Joint Mathematics Colloquium 

University of Idaho

Washington State University

Spring 2014

Thursday,  March 6, 3:30-4:20 pm, room TLC 149

Refreshments in Brink 305 at 3:00 pm

Hyperplane arrangements with low degree logarithmic vector fields


Stefan Tohaneanu

Department of Mathematics

   University of Idaho


We consider hyperplane arrangements that have logarithmic vector fields (or logarithmic derivations) of degree one or two, and which are not multiple of the Euler derivation. For the degree one case, by the means of edge ideals, we can show that the condition to have such a linear logarithmic derivation is equivalent to the hyperplane arrangement being reducible (i.e., Cartesian product of smaller arrangements). For the degree two case, as expected, the situation is not very nice. Though we were able to classify all hyperplane arrangements in the projective plane (line arrangements) that have a quadratic logarithmic derivation, the proof nor the classification do not give any insights on what happens in general.