Tutte seminar - Eric Katz

Line arrangements and intersection theory on algebraic surfaces

Abstract:

Line arrangements in the plane are an object of combinatorial and algebraic geometric interest. Their combinatorial analogues are rank 3 matroids. A line arrangement determines a particular algebraic surface. On this surface, one can study the intersection of curves, giving an intersection theory which encodes some of the geometry of the surface. This theory can be immediately extended to the abstract theory of rank 3 matroids. This gives a proof of the unimodality conjecture in this case. More significantly, it gives constraints on the structure of the Hasse diagram of the flat poset of the matroids making a connection with algebraic graph theory.

This work is joint with June Huh.