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

Departament de Matemàtiques

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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	Anglès
Pàgines (de-a)	193-206
Revista	Finite Fields and Their Applications
Volum	8
DOIs	https://doi.org/10.1006/ffta.2001.0335
Estat de la publicació	Publicada - 1 de gen. 2002

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10.1006/ffta.2001.0335

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title = "Orbits of galois invariant n-sets of ℙ1 under the action of PGL2",

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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author = "Amparo Lopez and Daniel Maisner and Enric Nart and Xavier Xarles",

year = "2002",

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doi = "10.1006/ffta.2001.0335",

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AU - Lopez, Amparo

AU - Maisner, Daniel

AU - Nart, Enric

AU - Xarles, Xavier

PY - 2002/1/1

Y1 - 2002/1/1

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

U2 - 10.1006/ffta.2001.0335

DO - 10.1006/ffta.2001.0335

M3 - Article

SN - 1071-5797

VL - 8

SP - 193

EP - 206

JO - Finite Fields and Their Applications

JF - Finite Fields and Their Applications

ER -

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

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