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On the Clifford algebra of a binary form


Author: Rajesh S. Kulkarni
Journal: Trans. Amer. Math. Soc. 355 (2003), 3181-3208
MSC (2000): Primary 16H05, 16G99, 14H40, 14K30
Published electronically: April 11, 2003
MathSciNet review: 1974681
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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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Additional Information

Rajesh S. Kulkarni
Affiliation: Department of Mathematics, University of Wisconsin-Madison, Madison, Wisconsin 53706
Address at time of publication: Department of Mathematics, Wells Hall, Michigan State University, East Lansing, Michigan 48824
Email: kulkarni@math.msu.edu

DOI: https://doi.org/10.1090/S0002-9947-03-03293-8
Received by editor(s): January 1, 2002
Published electronically: April 11, 2003
Article copyright: © Copyright 2003 American Mathematical Society