Generalized inflection points of very general effective divisors on smooth curves

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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.

Partially supported by the Fund of Scientific Research, Flanders (G.0318.06).