Determinantal resultant
Abstract
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, 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.
Cite
@article{arxiv.math/0209404,
title = {Determinantal resultant},
author = {Laurent Buse},
journal= {arXiv preprint arXiv:math/0209404},
year = {2007}
}
Comments
26 pages, 1 figure. LaTeX2e using amsart documentclass