On an extension of Galligo's theorem concerning the Borel-fixed points on the Hilbert scheme
| dc.creator | Sherman, Morgan | |
| dc.date | 2005-12-01 | |
| dc.date.accessioned | 2026-07-07T06:54:45Z | |
| dc.date.available | 2026-07-07T06:54:45Z | |
| dc.description | Given an ideal $I$ and a weight vector $w$ which partially orders monomials we can consider the initial ideal $\init_w (I)$ which has the same Hilbert function. A well known construction carries this out via a one-parameter subgroup of a $\GL_{n+1}$ which can then be viewed as a curve on the corresponding Hilbert scheme. Galligo \cite{galligo} proved that if $I$ is in generic coordinates, and if $w$ induces a monomial order up to a large enough degree, then $\init_w(I)$ is fixed by the action of the Borel subgroup of upper-triangular matrices. We prove that the direction the path approaches this Borel-fixed point on the Hilbert scheme is also Borel-fixed. | |
| dc.description | 22 pages | |
| dc.identifier | https://arxiv.org/abs/math/0512023 | |
| dc.identifier | http://arxiv.org/abs/math/0512023 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/106049 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 13P10; 14Q99 | |
| dc.title | On an extension of Galligo's theorem concerning the Borel-fixed points on the Hilbert scheme | |
| dc.type | text |