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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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On the Clifford algebra of a binary form
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by Rajesh S. Kulkarni PDF
Trans. Amer. Math. Soc. 355 (2003), 3181-3208 Request permission

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 $\operatorname {Pic}_{C/k}^{d + g - 1}$, 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
  • Received by editor(s): January 1, 2002
  • Published electronically: April 11, 2003
  • © Copyright 2003 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 355 (2003), 3181-3208
  • MSC (2000): Primary 16H05, 16G99, 14H40, 14K30
  • DOI: https://doi.org/10.1090/S0002-9947-03-03293-8
  • MathSciNet review: 1974681