Resultants of determinantal varieties

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 (Discriminants, Resultants, and Multidimensional Determinants, Birkhaüser, Boston, Basel, Berlin, 1994), 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 Lascoux (Adv. Math. 30 (1978) 202) 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.