The Hilbert scheme of points and its link with border basis


In this paper, we give new explicit representations of the Hilbert scheme of μ\mu points in \PP^{r} as a projective subvariety of a Grassmanniann variety. This new explicit description of the Hilbert scheme is simpler than the previous ones and global. It involves equations of degree 22. We show how these equations are deduced from the commutation relations characterizing border bases. Next, we consider infinitesimal perturbations of an input system of equations on this Hilbert scheme and describe its tangent space. We propose an effective criterion to test if it is a flat deformation, that is if the perturbed system remains on the Hilbert scheme of the initial equations. This criterion involves in particular formal reduction with respect to border bases

Similar works

Full text


INRIA a CCSD electronic archive server

Provided a free PDF
oaioai:HAL:inria-00433127v2Last time updated on 11/9/2016View original full text link

This paper was published in INRIA a CCSD electronic archive server.

Having an issue?

Is data on this page outdated, violates copyrights or anything else? Report the problem now and we will take corresponding actions after reviewing your request.