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arXiv · 0812.5013

Resultant as Determinant of Koszul Complex

A. Anokhina·A. Morozov·Sh. Shakirov
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Abstract

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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A. Anokhina, A. Morozov, Sh. Shakirov. 2008-12-30. Resultant as Determinant of Koszul Complex. https://doi.org/10.1007/s11232-009-0111-6

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