Some properties of Borel ideals (Q1295788)

Borel ideals appear as `generic initial ideals' of ideals \({\mathfrak a}\subseteq k[X_1,\dots,X_n]\). We analyse them paying special attention to the three variables case. In particular, we consider their Hilbert functions and minimal resolutions. Some features of a finite set \(\mathbb{X}\) of points in \(\mathbb{P}^r\) are investigated, by studying the Borel ideals that are generic initial ideals of \({\mathcal I}(\mathbb{X})\), with respect to deg-rev-lex ordering on monomials.