Symmetric Algebras and Factoriality

Computing the Integral Closure of an Affine Domain

“…We use a method developed in [11], exploiting the fact that the transform is computed relative to a two-generated ideal. There will be two steps to consider: Algorithm 2.6.…”

On the equations of Rees algebras.

“…We make use of the method of [44] and [45] to get the equations for the generators. To get /(2), we must add to (/, g, A, det5(cp)) these nine polynomials to begin with.…”

“…(/)), defined by the complement of F(/, g),/, g e R ( [45], Proposition l .2.1). s (/) are related by the fact that the latter is the ring of regulär functions on an open set of Spec(ä?…”

The symbolic defect of an ideal

“…We know of only a few papers that have studied the module I (m) /I m . This list includes: Arsie and Vatne's paper [3] which considers the Hilbert function of I (m) /I m ; Huneke's work [32] which considers P (2) /P 2 when P is a height two prime ideal in a local ring of dimension three; Herzog's paper [28] which studies the same family of ideals as Huneke using tools from homological algebra; Herzog and Ulrich's paper [29] and Vasconcelos's paper [41] which also consider a similar situation to Huneke, but with the assumption that P is generated by three elements; and Schenzel's work [38] which describes some families of prime ideals P of monomial curves with the property that P (2) /P 2 is cyclic (see the comment after [38,Theorem 2]).…”