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Journal Articles Journal of Pure and Applied Algebra Year : 2004

Resultants of determinantal varieties

Laurent Busé


In this paper, a new kind of resultant, called the determinantal resultant, is introduced. This operator computes the projection of a determinantal variety under suitable hypothesis. As a direct generalization of the resultant of a very ample vector bundle introduced by Gelfand, Kapranov et Zelevinsky, it corresponds to a necessary and sufficient condition so that a given morphism between two vector bundles on a projective variety X has rank lower or equal to a given integer in at least one point. First some conditions are given for the existence of such a resultant and it is showed how to compute explicitly its degree. Then a result of A. Lascoux is used to obtain it as a determinant of a certain complex. Finally some more detailed results in the particular case where X is a projective space are exposed.
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Dates and versions

inria-00098680 , version 1 (25-09-2006)


  • HAL Id : inria-00098680 , version 1


Laurent Busé. Resultants of determinantal varieties. Journal of Pure and Applied Algebra, 2004, 193 (1-3), pp.71--97. ⟨inria-00098680⟩
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