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ISSN 1088-6850(e) ISSN 0002-9947(p)

On the Clifford algebra of a binary form

Author(s): Rajesh S. Kulkarni
Journal: Trans. Amer. Math. Soc. 355 (2003), 3181-3208.
MSC (2000): Primary 16H05, 16G99, 14H40, 14K30
Posted: April 11, 2003
MathSciNet review: 1974681
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Abstract: The Clifford algebra of a binary form of degree is the -algebra $k\{x, y\}/I$ , where is the ideal generated by $\{(\alpha x + \beta y)^d - f(\alpha, \beta) \mid \alpha, \beta \in k\}$ . has a natural homomorphic image that is a rank 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 is the curve and is the genus of .

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