A new determinantal formula for the classical discriminant

Details A new determinantal formula for the classical discriminant A new determinantal formula for the classical discriminant

2008-12-05

arxiv.org/abs/0812.1197v2

Mathematics

Algebraic Geometry

22 pages, 2 figures

Scientific paper

According to several classical results by Bezout, Sylvester, Cayley, and others, the classical discriminant D_n of degree n polynomials may be expressed as the determinant of a matrix whose entries are much simpler polynomials in the coefficients of f. However, all of the determinantal formulae for D_n appearing in the classical literature are equivalent in the sense that the cokernels of their associated matrices are isomorphic as modules over the associated polynomial ring. This begs the question of whether there exist formulae which are not equivalent to the classical formulae and not trivial in the sense of having the same cokernel as the 1 x 1 matrix (D_n). In this paper, we construct an explicit non-classical formula: the presentation matrix of the open swallowtail first studied by Arnol'd and Givental. We study the properties of this formula, contrasting them with the properties of the classical formulae.

Affiliated with

Also associated with

No associations

Rating

A new determinantal formula for the classical discriminant does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A new determinantal formula for the classical discriminant, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A new determinantal formula for the classical discriminant will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-366122