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Orbits of Galois Invariant n-Sets of P1 under the Action of PGL2

✍ Scribed by Amparo López; Daniel Maisner; Enric Nart; Xavier Xarles

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 138 KB
Volume: 8
Category: Article
ISSN: 1071-5797
DOI: 10.1006/ffta.2001.0335

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✦ Synopsis

For any "nite "eld k we count the number of orbits of galois invariant n-sets of /(k M ) under the action of PGL (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)

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