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Mixed ladder determinantal varieties from two-sided ladders


Gorla, E (2007). Mixed ladder determinantal varieties from two-sided ladders. Journal of Pure and Applied Algebra, 211(2):433-444.

Abstract

We study the family of ideals defined by mixed size minors of two-sided ladders of indeterminates. We compute their Gröbner bases with respect to a skew-diagonal monomial order, then we use them to compute the height of the ideals. We show that these ideals correspond to a family of irreducible projective varieties, that we call mixed ladder determinantal varieties. We show that these varieties are arithmetically Cohen–Macaulay, and we characterize the arithmetically Gorenstein ones. Our main result consists in proving that mixed ladder determinantal varieties belong to the same G-biliaison class of a linear variety.

Abstract

We study the family of ideals defined by mixed size minors of two-sided ladders of indeterminates. We compute their Gröbner bases with respect to a skew-diagonal monomial order, then we use them to compute the height of the ideals. We show that these ideals correspond to a family of irreducible projective varieties, that we call mixed ladder determinantal varieties. We show that these varieties are arithmetically Cohen–Macaulay, and we characterize the arithmetically Gorenstein ones. Our main result consists in proving that mixed ladder determinantal varieties belong to the same G-biliaison class of a linear variety.

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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 07:32
Last Modified:05 Apr 2016 13:23
Publisher:Elsevier
ISSN:0022-4049
Publisher DOI:https://doi.org/10.1016/j.jpaa.2007.01.016
Related URLs:http://arxiv.org/abs/math/0510529

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Content: Accepted Version
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Download PDF  'Mixed ladder determinantal varieties from two-sided ladders'.
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Content: Accepted Version
Filetype: PDF (Accepted manuscript, Version 1)
Size: 219kB