Arithmetic inflection formulae for linear series on hyperelliptic curves

Ethan Cotterill, Ignacio Darago and Changho Han

Mathematische Nachrichten, 2023, vol. 296, issue 8, 3272-3300

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 A1$\mathbb {A}^1$‐homotopy theory for certain linear series on hyperelliptic curves defined over an arbitrary field.

Date: 2023
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https://doi.org/10.1002/mana.202100229

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