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

Research output: Contribution to journalArticleResearchpeer-review

7 Citations (Scopus)

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. © 2002 Elsevier Science (USA).
Original languageEnglish
Pages (from-to)193-206
JournalFinite Fields and Their Applications
Volume8
DOIs
Publication statusPublished - 1 Jan 2002

Keywords

  • Hyperelliptic curves
  • n-sets of projective spaces

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