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 projective dimension $r$ and degree $d$ on a curve of genus $g$. Here we explore the geometric meaning of a natural analogue of Plücker's formula in ${\mathbb{A}}^1$-homotopy theory for certain linear series on hyperelliptic curves defined over an arbitrary field.

Final, enhanced version, to appear in Math. Nachrichten; 30 pages, 4 figures

Cited by in corpus (2)

• Arithmetic inflection of superelliptic curves
• Conics meeting eight lines over perfect fields