Arithmetic inflection formulae for linear series on hyperelliptic curves

Abstract

Over the complex numbers, Plücker's formula computes the number of inflection points of a linear series of fixed degree and projective dimension on an algebraic curve of fixed genus. Here, we explore the geometric meaning of a natural analog of Plücker's formula and its constituent local indices in ‐homotopy theory for certain linear series on hyperelliptic curves defined over an arbitrary field.