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On the Clifford algebra of a binary form
Authors:Rajesh S. Kulkarni
Affiliation:Department of Mathematics, University of Wisconsin-Madison, Madison, Wisconsin 53706
Abstract:The Clifford algebra $C_f$ of a binary form $f$ of degree $d$is the $k$-algebra $k{x, y}/I$, where $I$ is the ideal generated by ${(alpha x + beta y)^d - f(alpha, beta) mid alpha, beta in k}$. $C_f$ has a natural homomorphic image $A_f$ that is a rank $d^2$ Azumaya algebra over its center. We prove that the center is isomorphic to the coordinate ring of the complement of an explicit $Theta$-divisor in $ensuremath{{Pic}_{C/k}^{d + g - 1}} $, where $C$ is the curve $(w^d - f(u, v))$ and $g$is the genus of $C$.

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