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The G-biliaison class of symmetric determinantal schemes


Gorla, E (2007). The G-biliaison class of symmetric determinantal schemes. Journal of Algebra, 310(2):880-902.

Abstract

We consider a family of schemes, that are defined by minors of a homogeneous symmetric matrix with polynomial entries. We assume that they have maximal possible codimension, given the size of the matrix and of the minors that define them. We show that these schemes are G-bilinked to a linear variety of the same dimension. In particular, they can be obtained from a linear variety by a finite sequence of ascending G-biliaisons on some determinantal schemes. We describe the biliaisons explicitly in the proof of Theorem 2.3. In particular, it follows that these schemes are glicci.

Abstract

We consider a family of schemes, that are defined by minors of a homogeneous symmetric matrix with polynomial entries. We assume that they have maximal possible codimension, given the size of the matrix and of the minors that define them. We show that these schemes are G-bilinked to a linear variety of the same dimension. In particular, they can be obtained from a linear variety by a finite sequence of ascending G-biliaisons on some determinantal schemes. We describe the biliaisons explicitly in the proof of Theorem 2.3. In particular, it follows that these schemes are glicci.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2007
Deposited On:11 Dec 2009 07:40
Last Modified:21 Nov 2017 14:21
Publisher:Elsevier
ISSN:0021-8693
Publisher DOI:https://doi.org/10.1016/j.jalgebra.2005.07.029
Related URLs:http://arxiv.org/abs/math/0505414v4

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Download PDF  'The G-biliaison class of symmetric determinantal schemes'.
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Content: Accepted Version
Filetype: PDF (Accepted manuscript, Version 2)
Size: 236kB
Download PDF  'The G-biliaison class of symmetric determinantal schemes'.
Preview
Content: Accepted Version
Filetype: PDF (Accepted manuscript, Version 1)
Size: 243kB