The determinantal ideals of extended Hankel matrices |
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Authors: | Le Dinh Nam |
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Institution: | Dipartimento di Matematica, Università degli Studi di Genova, Via Dodecaneso 35, 16146 Genova, Italy |
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Abstract: | In this paper, we use the tools of Gröbner bases and combinatorial secant varieties to study the determinantal ideals It of the extended Hankel matrices. Denote by c-chain a sequence a1,…,ak with ai+c<ai+1 for all i=1,…,k−1. Using the results of c-chain, we solve the membership problem for the symbolic powers and we compute the primary decomposition of the product It1?Itk of the determinantal ideals. Passing through the initial ideals and algebras we prove that the product It1?Itk has a linear resolution and the multi-homogeneous Rees algebra is defined by a Gröbner basis of quadrics. |
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Keywords: | Primary 13C40 Secondary 14M12 |
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