Orbits of Galois invariant \(n\)-sets of \(\mathbb P^ 1\) under the action of \(\text{PGL}_ 2\).

DOI10.1006/ffta.2001.0335zbMath1036.14011OpenAlexW2048728878MaRDI QIDQ1609399

Xavier Xarles, Amparo López, Daniel Maisner, Enric Nart Viñals

Publication date: 15 August 2002

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/ffta.2001.0335

zbMATH Keywords

finite ground fieldnumber of \(k\)-pointsnumber of hyperelliptic curvesnumber of orbits of Galois invariant \(n\)-sets

Mathematics Subject Classification ID

Group actions on varieties or schemes (quotients) (14L30) Enumerative problems (combinatorial problems) in algebraic geometry (14N10) Actions of groups on commutative rings; invariant theory (13A50) Finite ground fields in algebraic geometry (14G15)

Related Items (8)

On cyclic algebraic-geometry codes ⋮ Orbits of rational \(n\)-sets of projective spaces under the action of the linear group ⋮ On the number of curves of genus 2 over a finite field. ⋮ Counting hyperelliptic curves that admit a Koblitz model ⋮ Isometry classes of codes arising from sets of points in the projective plane ⋮ Abelian Surfaces over Finite Fields as Jacobians ⋮ Counting hyperelliptic curves ⋮ Hyperelliptic curves of genus three over finite fields of even characteristic

Cites Work

• Classification of Goppa codes of genus zero
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