Borel ideals appear as 'generic initial ideals' of ideals a subset of or eq
ual to k[X-1,...,X-n]. We analyse them paying special attention to the thre
e variables case. In particular, we consider their Hilbert functions and mi
nimal resolutions. Some features of a finite set X of points in P-r are inv
estigated, by studying the Borel ideals that are generic initial ideals of
F(X), will respect to deg-rev-lex ordering on monomials. (C) 1999 Published
by Elsevier Science B.V. All rights reserved.