Generalized inflection points of very general effective divisors on smooth curves

Abstract

Let E be a very general effective divisor of degree d on a smooth curve C of genus g. We study inflection points on linear systems |aE | for an integer a ≥ 1. They are called generalized inflection points of the invertible sheaf \({\mathcal{O}_C(E)}\). In case \({P\notin E}\) is a generalized inflection point of \({\mathcal{O}_C(E)}\) then it is a normal generalized inflection point. In case \({P\in E}\) then P has minimal vanishing sequences for E.