Rees algebras and almost linearly presented ideals

Abstract

Abstract. Consider a grade 2 perfect idealwhich is generated by forms of the same degree. Assume that the presentation matrix ϕ is almost linear, that is, all but the last column of ϕ consist of entries which are linear. For such ideals, we find explicit forms of the defining ideal of the Rees algebra R(I). We also introduce the notion of iterated Jacobian duals.

On Rees algebras of ideals and modules over hypersurface rings

“…, x d+1 with the exception of f . In [2] this same phenomenon occurred, but was due to a column of nonlinear entries in a presentation matrix. With this, we proceed along a similar path to study A, but must frequently take alternative approaches for the proofs presented here.…”

“…With this, we proceed along a similar path to study A, but must frequently take alternative approaches for the proofs presented here. In [2] the saturation encountered was a prime ideal, an assumption crucial for Boswell and Mukundan's arguments and one we do not necessarily possess unless f is irreducible.…”

“…The saturation A is reminiscent of a similar ideal encountered in [2]. Observe that the generators of L are all linear with respect to x 1 , .…”

“…, x d ]. In [2] Boswell and Mukundan extended this to the case where I is again a perfect ideal of grade 2 of k[x 1 , . .…”

The equations defining blowup algebras of height three Gorenstein ideals

“…There has been a great deal of work investigating the defining ideal of Rees rings when I is a height two perfect ideal that either fails to satisfy G d or is not linearly presented. In this case R (I) usually does not have the expected form and is not Cohen-Macaulay; see for instance [27,15,35,10,13,36,48,14,5,44].…”