Enumerative geometry of curves with exceptional secant planes

We study curves with linear series that are exceptional with
regard to their secant planes. Working in the framework of an extension of Brill-Noether theory to pairs of linear series, we prove that a general curve of genus g has no exceptional secant planes, in a sense we will make precise. We also compute the classes of divisors associated to exceptional
secant plane behavior in the Picard group of the moduli space of curves in a couple of naturally-arising infinite families of cases.