Gorenstein algebras, symmetric matrices, self-linked ideals, and symbolic powers

dc.creatorKleiman, Steven
dc.creatorUlrich, Bernd
dc.date1995-09-10
dc.date.accessioned2026-07-07T09:06:37Z
dc.date.available2026-07-07T09:06:37Z
dc.descriptionInspired 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.descriptionAmS-TeX-Ver 2.1 with amsppt.sty-ver 2.1c, 32 pages
dc.identifierhttps://arxiv.org/abs/alg-geom/9509005
dc.identifierhttp://arxiv.org/abs/alg-geom/9509005
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/150073
dc.subjectAlgebraic Geometry
dc.subjectCommutative Algebra
dc.subject13C40, 13H10, 13A30, 14E05
dc.titleGorenstein algebras, symmetric matrices, self-linked ideals, and symbolic powers
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