Gorenstein algebras, symmetric matrices, self-linked ideals, and symbolic powers
| dc.creator | Kleiman, Steven | |
| dc.creator | Ulrich, Bernd | |
| dc.date | 1995-09-10 | |
| dc.date.accessioned | 2026-07-07T09:06:37Z | |
| dc.date.available | 2026-07-07T09:06:37Z | |
| dc.description | Inspired by recent work in the theory of central projections onto hypersurfaces, we characterize self-linked perfect ideals of grade 2 as those with a Hilbert--Burch matrix that has a maximal symmetric subblock. We also prove that every Gorenstein perfect algebra of grade 1 can be presented, as a module, by a symmetric matrix. Both results are derived from the same elementary lemma about symmetrizing a matrix that has, modulo a nonzerodivisor, a symmetric syzygy matrix. In addition, we establish a correspondence, roughly speaking, between Gorenstein perfect algebras of grade 1 that are birational onto their image, on the one hand, and self-linked perfect ideals of grade 2 that have one of the self-linking elements contained in the second symbolic power, on the other hand. Finally, we provide another characterization of these ideals in terms of their symbolic Rees algebras, and we prove a criterion for these algebras to be normal. | |
| dc.description | AmS-TeX-Ver 2.1 with amsppt.sty-ver 2.1c, 32 pages | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9509005 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9509005 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/150073 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13C40, 13H10, 13A30, 14E05 | |
| dc.title | Gorenstein algebras, symmetric matrices, self-linked ideals, and symbolic powers | |
| dc.type | text |