Abeliants and their application to an elementary construction of Jacobians

Greg W. Anderson

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)169-205
Number of pages37
JournalAdvances in Mathematics
Issue number2
StatePublished - Dec 25 2002


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