Abeliants and their application to an elementary construction of Jacobians |
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Authors: | Greg W Anderson |
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Institution: | School of Mathematics, University of Minnesota, Vincent Hall, 206 Church St. SE, Minneapolis, MN 55455, USA |
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Abstract: | The abeliant is a polynomial rule which to each n×n by n+2 array with entries in a commutative ring with unit associates an n×n matrix with entries in the same ring. The theory of abeliants, first introduced in an earlier paper of the author, is simplified and extended here. Now let J be the Jacobian of a nonsingular projective algebraic curve defined over an algebraically closed field. With the aid of the theory of abeliants we obtain explicit defining equations for J and its group law. |
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Keywords: | 14H40 14Q05 |
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