English

On Rees algebras of 2-determinantal ideals

Commutative Algebra 2024-06-06 v2 Algebraic Geometry

Abstract

Let I be the ideal of minors of a 2 by n matrix of linear forms with the expected codimension. In this paper we prove that the Rees algebra of I and its special fiber ring are Cohen-Macaulay and Koszul; in particular, they are quadratic algebras. The main novelty in our approach is the analysis of a stratification of the Hilbert scheme of determinantal ideals. We study degenerations of Rees algebras along this stratification, and combine it with certain squarefree Groebner degenerations.

Keywords

Cite

@article{arxiv.2210.12668,
  title  = {On Rees algebras of 2-determinantal ideals},
  author = {Ritvik Ramkumar and Alessio Sammartano},
  journal= {arXiv preprint arXiv:2210.12668},
  year   = {2024}
}

Comments

Final version. To appear on the Journal of the London Mathematical Society