On the Hilbert scheme of varieties defined by maximal minors

TL;DR

This paper calculates the dimension of the Hilbert scheme for certain subvarieties in projective space defined by maximal minors of polynomial matrices, advancing understanding of their geometric properties.

Contribution

It provides a precise computation of the Hilbert scheme dimension for varieties defined by maximal minors, a previously less understood class.

Findings

Dimension of the Hilbert scheme explicitly computed.

Results apply to subvarieties defined by maximal minors.

Enhances understanding of the geometry of determinantal varieties.

Abstract

We compute the dimension of the Hilbert scheme of subvarieties of positive dimension in projective space which are cut by maximal minors of a matrix with polynomial entries.