2001/12/05 by Greg W. Anderson, Anderson, Greg W. · 1 citation
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Commutative Algebra and Its Applications #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation #math.NT
paper · pdf · doi:10.48550/arxiv.math/0112321
arxiv created 2001/12/05 · openalex publication_date 2001/12/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.