| Given a fixed binary form f(u, v) of degree d over a field k, the associated Clifford algebra is the k-algebra C f = k{u, v}/I, where I is the two-sided ideal generated by elements of the form (alphau + betav) d - f(alpha, beta) with alpha and beta arbitrary elements in k. All representations of Cf have dimensions that are multiples of d, and occur in families. In this article we construct fine moduli spaces U = Uf,r for the rd-dimensional representations of Cf for each r ≥ 2. Our construction starts with the projective curve C ⊂ P2k defined by the equation wd = f (u, v), and produces Uf,r as a quasiprojective variety in the moduli space M (r, dr) of stable vector bundles over C with rank r and degree dr = r(d + g - 1), where g denotes the genus of C. |
