TY - JOUR
T1 - Nonsingular deformations of a determinantal scheme
AU - Schaps, Mary
PY - 1976/7
Y1 - 1976/7
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84972537479&partnerID=8YFLogxK
U2 - 10.2140/pjm.1976.65.209
DO - 10.2140/pjm.1976.65.209
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AN - SCOPUS:84972537479
SN - 0030-8730
VL - 65
SP - 209
EP - 215
JO - Pacific Journal of Mathematics
JF - Pacific Journal of Mathematics
IS - 1
ER -