Linear resolutions and Gröbner basis of Hankel determinantal ideals

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 $I_1\dots I_l$ of ideals of $f$ has linear resolution. Moreover, we show that natural generators of every product $I_1\dots I_l$ form a Gröbner basis.