Enriched inflection and secant planes for linear series on algebraic curves

The fundamental local invariant of a linear series on an algebraic curve is its inflection, as measured by the vanishing of local derivatives in a point. Secant planes, which emerge from the rank behavior of tuples of points on the curve, may be regarded as (the manifestations of) a global analogue of inflection. Here we report on joint work with Ignacio Darago and Naizhen Zhang in which we compute the classes of inflection points and of tuples of points spanning secant planes in the Grothendieck--Witt ring of an arbitrary perfect base field of characteristic not equal to 2.