Trigonal curves and Galois Spin(8)-bundles
Abstract
Let SUC(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 NC containing SUC(2) as a subvariety and smooth of dimension 7g-14 away from SUC(2). NC parametrises Galois Spin(8)-bundles on the Galois closure of C over P1. Moreover, if x in JC[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 SUR(x)(2) into NC giving a `nonabelian Schottky configuration' in NC singular along the classical Schottky configuration in SUC(2).
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