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

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

1995-09-10

arxiv.org/abs/alg-geom/9509005v1

Mathematics

Commutative Algebra

AmS-TeX-Ver 2.1 with amsppt.sty-ver 2.1c, 32 pages

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Gorenstein algebras, symmetric matrices, self-linked ideals, and symbolic powers does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Gorenstein algebras, symmetric matrices, self-linked ideals, and symbolic powers, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Gorenstein algebras, symmetric matrices, self-linked ideals, and symbolic powers will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-280588