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).
- Hyperelliptic curves
- n-sets of projective spaces