Some properties of Borel ideals

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.