Standard and Weierstrass spin groups on hyperelliptic Riemann surfaces

Abstract

We show that at any standard or Weierstrass point P on a hyperelliptic Riemann surface S equipped with a nonsingular even spin structure, we may attach a spin group G(P) in a natural way. All such spin groups are isomorphic to each other and to the alternating group A(g)<S(g). Moreover, for any two vertices of the same spin graph we construct a natural, unique isomorphism between the corresponding, mutually conjugate spin groups.