Arithmetic inflection formulae for linear series on hyperelliptic curves

TL;DR

This paper investigates a geometric analogue of Plücker's formula within $\

Contribution

It extends classical inflection point counts to hyperelliptic curves over arbitrary fields using $\

Findings

Provides a new $\

Establishes a link between $\

Generalizes classical results to broader algebraic settings.

Abstract

Over the complex numbers, Pl\"ucker's formula computes the number of inflection points of a linear series of projective dimension $r$ and degree $d$ on a curve of genus $g$. Here we explore the geometric meaning of a natural analogue of Pl\"ucker's formula in $\mathbb{A}^1$-homotopy theory for certain linear series on hyperelliptic curves defined over an arbitrary field.