Geodesic
Resultant as the~determinant of a~Koszul complex
Teoretičeskaâ i matematičeskaâ fizika, Tome 160 (2009) no. 3, pp. 403-433

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The determinant is a very important characteristic of a linear map between vector spaces. Two generalizations of linear maps are intensively used in modern theory: linear complexes (nilpotent chains of linear maps) and nonlinear maps. The determinant of a complex and the resultant are then the corresponding generalizations of the determinant of a linear map. It turns out that these two quantities are related: the resultant of a nonlinear map is the determinant of the corresponding Koszul complex. We give an elementary introduction into these notions and relations, which will definitely play a role in the future development of theoretical physics.
Keywords: resultant, nonlinear algebra.
Mots-clés : Koszul complex 
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     title = {Resultant as the~determinant of {a~Koszul} complex},
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A. S. Anokhina; A. Yu. Morozov; Sh. R. Shakirov. Resultant as the~determinant of a~Koszul complex. Teoretičeskaâ i matematičeskaâ fizika, Tome 160 (2009) no. 3, pp. 403-433. http://geodesic.mathdoc.fr/item/TMF_2009_160_3_a0/