Arithmetic inflection formulae for linear series on hyperelliptic curves. (English) Zbl 1537.14034
Summary: 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 \(\mathbb{A}^1\)-homotopy theory for certain linear series on hyperelliptic curves defined over an arbitrary field.
{© 2023 Wiley-VCH GmbH.}
{© 2023 Wiley-VCH GmbH.}
MSC:
| 14F42 | Motivic cohomology; motivic homotopy theory |
| 14C20 | Divisors, linear systems, invertible sheaves |
| 14C35 | Applications of methods of algebraic \(K\)-theory in algebraic geometry |
| 11G25 | Varieties over finite and local fields |
| 14N10 | Enumerative problems (combinatorial problems) in algebraic geometry |
| 19E15 | Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects) |
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