On the Clifford Algebra of a Binary Form

The Clifford algebra Cf of a binary form f of degree d is the kalgebra k{x, y}/I, where I is the ideal generated by {(αx + βy)d − f(α, β) | α, β ∈ k}. Cf has a natural homomorphic image Af that is a rank d2 Azumaya algebra over its center. We prove that the center is isomorphic to the coordinate ring of the complement of an explicit Θ-divisor in Picd+g−1 C/k , where C is the curve (wd − f(u, v)) and g is the genus of C.