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.
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机译：给定在字段k上度为d的固定二进制形式f（u，v），则相关的Clifford代数为k代数C f = k {u，v} / I，其中I是由形式（alphau + betav）d-f（alpha，beta）的元素，其中k和alpha和beta任意元素。 Cf的所有表示形式都具有d的倍数，并且以族出现。在本文中，我们为每个r≥2的Cf的三维表示构造了精细的模空间U = Uf，r。我们的构建始于方程wd = f（u，v）定义的投影曲线C⊂P2k，并在C上具有秩r和度dr = r（d + g-1）的C上稳定矢量束的模空间M（r，dr）中产生准投影变体Uf，r，其中g表示C的属。
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