  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.

Commutative Algebra;Algebraic Geometry