Generalized inflection points of very general effective divisors on smooth curves

摘要

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 O_C(E){mathcal{O}_C(E)}. In case P Ï E{Pnotin E} is a generalized inflection point of O_C(E){mathcal{O}_C(E)} then it is a normal generalized inflection point. In case P Î E{Pin E} then P has minimal vanishing sequences for E.