Algebra seminar - A. Zanardini MSc University of Pennsylvania

Title: Stability of pencils of plane curves

Abstract:

In this talk I will discuss some recent results on the problem of classifying pencils of plane curves via geometric invariant theory. We will see how the stability of a pencil is related to the stability of its generators, to the log canonical threshold, and to the multiplicities of a base point. In particular, I will present some results on the stability of certain pencils of plane sextics called Halphen pencils of index two.