Hilbert schemes with two Borel-fixed points in arbitrary characteristic

Untitled

“…, x n ], where in this appendix k may have any characteristic. Let B = B(n + 1) be the Borel subgroup of upper triangular matrices of G = GL(n + 1), those invertible linear maps sending x j → j i=1 α ij x i , where the α ij ∈ k. An ideal Galligo's theorem [21] that any ideal degenerates to a Borel ideal and Theorem C.1 are inspiration for approaches to the classification of Hilbert scheme components using Borel ideals, [8], [12,19,29], and recently [41,45].…”

“…0) degenerates to such an ideal, [21] or see [14,Sec.15.9]. Also called Borel-fixed ideals, they are a way to understand and classify components of the Hilbert scheme, [7,8,12,19,29,41,42,45]. They are the most degenerate of homogeneous ideals in polynomial rings k[x 1 , .…”