14 citations · 15 across the 7 of their papers we have counts for
5 papers · 1 filter
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…
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…