Abeliants and their application to an elementary construction of Jacobians

Details Abeliants and their application to an elementary construction of Jacobians Abeliants and their application to an elementary construction of Jacobians

2001-12-05

arxiv.org/abs/math/0112321v1

Mathematics

Number Theory

Scientific paper

The {\em abeliant} is a polynomial rule for producing an $n$ by $n$ matrix with entries in a given ring from an $n$ by $n$ by $n+2$ array of elements of that ring. The theory of abeliants, first introduced in an earlier paper of the author, is redeveloped here in a simpler way. Then this theory is exploited to give an explicit elementary construction of the Jacobian of a nonsingular projective algebraic curve defined over an algebraically closed field. The standard of usefulness and aptness we strive toward is that set by Mumford's elementary construction of the Jacobian of a hyperelliptic curve. This paper has appeared as Advances in Math 172 (2002) 169-205.

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