Trigonal curves and Galois Spin(8)-bundles

1999/07/19 by W. M. Oxbury, S. Ramanan, Oxbury, W. M. +1 · 1 citation
Mathematics · Physics and Astronomy · #14D20 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Nonlinear Waves and Solitons #math.AG #msc:14D20

paper · pdf · doi:10.48550/arxiv.math/9907114

LaTeX2e, 39 pages with 6 figures

arxiv created 1999/07/19 · openalex publication_date 1999/07/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 P¹. 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).

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