On discriminants of polylinear forms

Abstract

In this paper we propose a conseptual framework for the observed properties of discriminants of polylinear forms. The connection with classical problems of linear algebra is shown. A new class of algebraic varieties (hypergrassmanians) is introduced, the particular case of which are grassman manifolds. An algorithm is given for computing the discriminants of polylinear forms of "boundary format" (hypergrassmanian analogues of plukker coordinates). The algorithm for computing the discriminants of polylinear forms of general formats is outlined.