Trigonal curves and Galois Spin(8)-bundles

Abstract

Let SU_C(2) denote the moduli variety of rank 2 semistable vector bundles with trivial determinant on an algebraic curve C. We prove that if C is trigonal then there exists a projective moduli variety N_C containing SU_C(2) as a subvariety and smooth of dimension 7g-14 away from SU_C(2). N_C parametrises Galois Spin(8)-bundles on the Galois closure of C over P^1. Moreover, if x in J_C[2] is a 2-torsion point let R(x) be the Recillas tetragonal curve whose Jacobian is isomorphic to Prym(C,x). Then there is an injection of SU_R(x)(2) into N_C giving a `nonabelian Schottky configuration' in N_C singular along the classical Schottky configuration in SU_C(2).