Nonsingular deformations of a determinantal scheme

Mary Elizabeth Schaps

Vol. 65 (1976), No. 1, 209–215

DOI: 10.2140/pjm.1976.65.209

Abstract

We will be considering an affine algebraic scheme X over a field k, which is determinantal, defined by the vanishing of the l × l minors of a matrix R.

We will show that deforming the constant and linear terms of the entries in the matrix R gives an almost everywhere flat deformation of X, and that under certain simple conditions, and in particular if the dimension of X is sufficiently low, this deformation has generically nonsingular fibers.

Mathematical Subject Classification 2000

Primary: 14D15

Milestones

Received: 20 January 1975

Revised: 10 February 1976

Published: 1 July 1976