Linear resolutions and Gröbner basis of Hankel determinantal ideals

2018/10/04 by Jafari, Sepehr
#13D02 #15A15 #16S80 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1810.02139

Abstract

In this paper, we study the family of determinantal ideals of "close" cuts of Hankel matrices, say f . We show that the multi-Rees algebra of ideals in f is defined by a quadratic Gröbner 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 I₁… I_l of ideals of f has linear resolution. Moreover, we show that natural generators of every product I₁… I_l form a Gröbner basis.

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