On Hilbert covariants

Details On Hilbert covariants On Hilbert covariants

2012-03-21

arxiv.org/abs/1203.4761v1

Mathematics

Algebraic Geometry

27 pages

Scientific paper

Let F denote a binary form of order d over the complex numbers. If r is a divisor of d, then the Hilbert covariant H_{r,d}(F) vanishes exactly when F is the perfect power of an order r form. In geometric terms, the coefficients of H give defining equations for the image variety X of an embedding P^r->P^d. In this paper we describe a new construction of the Hilbert covariant; and simultaneously situate it into a wider class of covariants called the G\"ottingen covariants, all of which vanish on X. We prove that the ideal generated by the coefficients of H defines X as a scheme. Finally, we exhibit a generalisation of the G\"ottingen covariants to n-ary forms using the classical Clebsch transfer principle.

Affiliated with

Also associated with

No associations

Rating

On Hilbert covariants 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 On Hilbert covariants, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On Hilbert covariants will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-488744