Orbits of galois invariant n-sets of ℙ<sup>1</sup> under the action of PGL<inf>2</inf>

Amparo Lopez; Daniel Maisner; Enric Nart; Xavier Xarles

doi:10.1006/ffta.2001.0335

Orbits of galois invariant n-sets of ℙ<sup>1</sup> under the action of PGL<inf>2</inf>

Amparo Lopez, Daniel Maisner, Enric Nart, Xavier Xarles

Departamento de Matemáticas

Producción científica: Contribución a una revista › Artículo › Investigación › revisión exhaustiva

8 Citas (Scopus)

Resumen

For any finite field k we count the number of orbits of galois invariant n-sets of ℙ1(k) under the action of PGL2 (k). For k of odd characteristic, this counts the number of k-points of the moduli space of hyperelliptic curves of genus g over k. We get in this way an explicit formula for the number of hyperelliptic curves over k of genus g, up to k-isomorphism and quadratic twist. © 2002 Elsevier Science (USA).

Idioma original	Inglés
Páginas (desde-hasta)	193-206
Publicación	Finite Fields and Their Applications
Volumen	8
DOI	https://doi.org/10.1006/ffta.2001.0335
Estado	Publicada - 1 ene 2002

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abstract = "For any finite field k we count the number of orbits of galois invariant n-sets of ℙ1(k) under the action of PGL2 (k). For k of odd characteristic, this counts the number of k-points of the moduli space of hyperelliptic curves of genus g over k. We get in this way an explicit formula for the number of hyperelliptic curves over k of genus g, up to k-isomorphism and quadratic twist. {\textcopyright} 2002 Elsevier Science (USA).",

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N2 - For any finite field k we count the number of orbits of galois invariant n-sets of ℙ1(k) under the action of PGL2 (k). For k of odd characteristic, this counts the number of k-points of the moduli space of hyperelliptic curves of genus g over k. We get in this way an explicit formula for the number of hyperelliptic curves over k of genus g, up to k-isomorphism and quadratic twist. © 2002 Elsevier Science (USA).

AB - For any finite field k we count the number of orbits of galois invariant n-sets of ℙ1(k) under the action of PGL2 (k). For k of odd characteristic, this counts the number of k-points of the moduli space of hyperelliptic curves of genus g over k. We get in this way an explicit formula for the number of hyperelliptic curves over k of genus g, up to k-isomorphism and quadratic twist. © 2002 Elsevier Science (USA).

KW - Hyperelliptic curves

KW - n-sets of projective spaces

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DO - 10.1006/ffta.2001.0335

M3 - Article

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JO - Finite Fields and Their Applications

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ER -

Orbits of galois invariant n-sets of ℙ<sup>1</sup> under the action of PGL<inf>2</inf>

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