交换子及其在Jacobian初等构造中的应用
Abeliants and their application to an elementary construction of Jacobians
摘要：
{ \em abeliant}是用于从给定环的元素的$n$ × $n$ × $n+2$阵列产生具有该环中的条目的$n$ × $n$矩阵的多项式规则。在作者的早期论文中首次介绍的abeliants理论，在这里以一种更简单的方式重新开发。然后利用这一理论给出了定义在代数闭域上的非奇异射影代数曲线的雅可比矩阵的显式初等构造。我们努力追求的有用性和适当性的标准是由芒福德对超椭圆曲线的雅可比矩阵的初等构造所确定的。这篇论文发表在Advances in Math 172（2002）169-205中。
英文摘要：
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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