Quadratic Gröbner bases of block diagonal matching field ideals and toric degenerations of Grassmannians

Abstract

In the present paper, we prove that the toric ideals of certain $s$-block diagonal matching fields have quadratic Gröbner bases. Thus, in particular, those are quadratically generated. By using this result, we provide a new family of toric degenerations of Grassmannians.

arXiv comment15 pages; J. Pure Appl. Algebra, to appear