Resultant as Determinant of Koszul Complex

Details Resultant as Determinant of Koszul Complex Resultant as Determinant of Koszul Complex

2008-12-30

arxiv.org/abs/0812.5013v3

Theor.Math.Phys. 160:3 (2009) 1203-1228

Physics

Mathematical Physics

32 pages, 12 figures

Scientific paper

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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