On Rees algebras of 2-determinantal ideals

Let I$I$ be the ideal of minors of a 2xn$2 \times n$ matrix of linear forms with the expected codimension. In this paper, we prove that the Rees algebra of I$I$ 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 Grobner degenerations.