14 citations · 15 across the 7 of their papers we have counts for
8 papers
The Complete Intersection Discrepancy of a Curve I: Numerical Invariants
Andrei Benguş-Lasnier, Antoni Rangachev
We generalize two classical formulas for complete intersection curves by introducing the complete intersection discrepancy of a curve as a correction term. The first is a well-know…
The Complete Intersection Discrepancy of a Curve II: Families of Curves
Andrei Benguş-Lasnier, Terence Gaffney, Antoni Rangachev
We study equisingularity of families of reduced curves over smooth parameter spaces of arbitrary positive dimension, using the difference between two analytic invariants of a curve…
Local volumes, equisingularity, and generalized smoothability
Antoni Rangachev
We introduce the restricted local volume of a relatively very ample invertible sheaf as an invariant of equisingularity by determining its change across families. We apply this res…
A valuation theorem for Noetherian rings
Antoni Rangachev
Let A and B be integral domains. Suppose A is Noetherian and B is a finitely generated A-algebra that contains A. Denote by A' the integral closure of A in B. We show that A' is de…
Associated primes and integral closure of Noetherian rings
Antoni Rangachev
Let A be a Noetherian ring and B be a finitely generated A-algebra. Denote by A' the integral closure of A in B. We give necessary and sufficient conditions for prime ideals to be…
The A_f condition and relative conormal spaces for functions with non-vanishing derivative
Terence Gaffney, Antoni Rangachev
We introduce a join construction as a way of completing the description of the relative conormal space of an analytic function on a complex analytic space that has a non-vanishing…
Associated points and integral closure of modules
Antoni Rangachev
Let be an affine Noetherian scheme, and be a pair of finitely generated -modules. Denote their Rees algebras by $\mathcal…
Pairs of modules and determinantal isolated singularities
Terence Gaffney, Antoni Rangachev
We continue the development of the study of the equisingularity of isolated singularities, in the determinantal case. This version of the paper includes a substantial amount of new…