arXiv subjects

Andrei Benguş-Lasnier

Publications and source records attributed to Andrei Benguş-Lasnier.

3 recordsLinked to original sources

arXiv2026

The Complete Intersection Discrepancy of a Curve I: Numerical Invariants

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-known multiplicity formula in singularity theory, due to Lê, Greuel and Teissier, which relates some of the basic invariants of a curve singularity. We apply this generalization elsewhere to the study of equisingularity of curves. The second is the genus--degree formula for projective curves. The main technical tool used to obtain these generalizations is an adjunction-type identity derived from Grothendieck duality theory.

math.AG↗

arXiv2026

The Complete Intersection Discrepancy of a Curve II: Families of Curves

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 singularity: the multiplicity of its Jacobian ideal and its complete intersection discrepancy. This difference provides a fiberwise multiplicity criterion for Whitney equisingularity. We prove that Whitney equisingularity (equivalently, strong simultaneous resolution) is characterized by equidimensionality of the fibers of the exceptional locus of either the relative conormal space or the relative Nash blowup. We further show that this condition is equivalent to the emptiness of the relative polar variety of smallest dimension. In addition, we establish that the Milnor number of a reduced curve is Zariski upper semicontinuous. As an application, we show that the constancy of the Milnor number in a family of reduced curves is equivalent to its topological equisingularity.

math.AG↗

arXiv2021

Minimal Pairs, Truncations and Diskoids

We build on the correspondence between abstract key polynomials and minimal pairs made by Novacoski and show how to relate the valuations that are generated by each object. We can then give a geometric interpretation of valuations built in this fashion. To do so we employ an object called diskoid, which is a generalisation of the classical concept of ball in non-archimedian valued fields.

math.AC↗