Derivations and integral closure

Derivations and the Integral Closure of Ideals

Let (R, m) be a complete local domain containing the rationals. Then there exists an integer l such that for any ideal I ⊆ R, if f ∈ m, f / ∈ In, then there exists a derivation δ of R with δ(f) / ∈ In+l. This note grew out of a question raised by C. Huneke some years ago: Suppose (R, m) is a complete local domain with perfect residue class field k which it contains. Call an element x ∈ R deriva...

Specialization and integral closure

I ′/(x) = I ′/(x) , where x = ∑n i=1 ziai is a generic element for I defined over the polynomial ring R ′ = R[z1, . . . , zn] and I ′ denotes the extension of I to R. This result can be paraphrased by saying that an element is integral over I if it is integral modulo a generic element of the ideal. Other, essentially unrelated, results about lifting integral dependence have been proved by Teiss...

Computing Integral Closure Workshop

Real Integral Closure and Milnor Fibrations

We give a condition to guarantee the existence of a Milnor fibration for real map germs of corank 1, which include cases that are not L-maps in the sense of Massey. Our approach exploits the structure of a family of functions.

Nilpotents, Integral Closure and Equisingularity conditions