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arXiv · 1810.02139

Linear resolutions and Gr\"{o}bner basis of Hankel determinantal ideals

Sepehr Jafari
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Abstract

In this paper, we study the family of determinantal ideals of "close" cuts of Hankel matrices, say $ \mathcal{f} $. We show that the multi-Rees algebra of ideals in $ \mathcal{f} $ is defined by a quadratic Gr\"{o}bner basis, it is Koszul, normal Cohen-Macaulay domain and it has a nice Sagbi basis. As a consequence of Koszulness, we prove that every product $ I_1\ldots I_l $ of ideals of $ \mathcal{f} $ has linear resolution. Moreover, we show that natural generators of every product $ I_1\ldots I_l $ form a Gr\"{o}bner basis.

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Sepehr Jafari. 2018-10-04. Linear resolutions and Gr\"{o}bner basis of Hankel determinantal ideals. https://arxiv.org/abs/1810.02139

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