The initial algebra of maximal minors of a generalized hankel matrix |
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Authors: | Paulo F Machado |
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Institution: | Depto. de Matemática, TCEX , Universidade Federal de Minas Cerais , Belo Horizonte, MC, 30161-970, Brazil E-mail: pafm@mat.ufrag.br |
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Abstract: | One deals with a certain generalization of the (generic) Hankel matrix. Fixing a field K, for a suitable diagonal term order on the polynomial ring B over K generated by the entries of this matrix, one considers the K-subalgebra A ? B generated by the set of initial terms of the the maximal minors of the matrix. The algebra A detects the underlying combinatorics in terms of certain generalized standard tableaux and these give a way of showing that A is normal. A more involved technique also yields that the Rees algebra of the ideal of B generated by the generators of A is normal. In particular, both algebras are Cohen-Macaulay. We also present a Gröbner basis for the presentation ideal of A and compute some numerical invariants using the simplicial complex associated to A. |
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