结式作为Koszul复形的行列式
Resultant as Determinant of Koszul Complex
摘要：
两个向量空间之间的线性映射有一个非常重要的特征：行列式。在现代理论中，线性映射的两种推广被广泛使用：线性复形（线性映射的幂零链）和非线性映射。相应地，线性映射的行列式有两种推广：复形行列式和结式行列式。这些量实际上是相关的：一个非线性映射的结式是相应的Koszul复形的行列式。本文对这些概念及其相互关系作了初步的介绍，这对今后理论物理的发展必将起到一定的作用。
英文摘要：
A linear map between two vector spaces has a very important characteristic: a determinant. In modern theory two generalizations of linear maps are intensively used: to linear complexes (the nilpotent chains of linear maps) and to non-linear mappings. Accordingly, determinant of a linear map has two generalizations: to determinants of complexes and to resultants. These quantities are in fact related: resultant of a non-linear map is determinant of the corresponding Koszul complex. We give an elementary introduction into these notions and interrelations, which will definitely play a role in the future development of theoretical physics.
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