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Arithmetic inflection formulae for linear series on hyperelliptic curves

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  • Ethan Cotterill
  • Ignacio Darago
  • Changho Han

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.

Suggested Citation

  • Ethan Cotterill & Ignacio Darago & Changho Han, 2023. "Arithmetic inflection formulae for linear series on hyperelliptic curves," Mathematische Nachrichten, Wiley Blackwell, vol. 296(8), pages 3272-3300, August.
    • Handle: RePEc:bla:mathna:v:296:y:2023:i:8:p:3272-3300
    DOI: 10.1002/mana.202100229
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