Searcharxiv⌕ Search

arXiv subjects

Anca Măcinic

Publications and source records attributed to Anca Măcinic.

5 recordsLinked to original sources
arXiv2026

On modular inequalities for plane projective curves

We introduce modular inequalities for complements of plane curves, based on a Combinatorial Aomoto complex construction associated with the weak combinatorial type of a curve. We use this as a tool to investigate twisted Alexander polynomials, in particular to study the characteristic polynomial of the Milnor fiber associated to a projective plane curve, i.e. the classical Alexander polynomial. We give criteria for the non-triviality of the resonance in degree $1$, over a positive characteristic field, for curves with quasi fiber--type structure and we compute lower bounds for the multiplicities of some roots of twisted Alexander polynomials for this type of curves. We apply these results to theoretically compute the multiplicities of certain roots of twisted Alexander polynomials for fiber--type curves.

math.AT↗
arXiv2025

Addition-deletion for conic-line arrangements with split Chern polynomial

We present combinatorial/geometric obstructions induced by the factorization over the integers of the Chern polynomial of the bundle of logarithmic vector fields associated to a complex projective plane curve. Our results generalize at the same time similar results on projective lines arrangements whose characteristic polynomial factors over the integers and results on free curves. We give a splitting criterion for a rank 2 vector bundle, in terms of restrictions to smooth conics.

math.AG↗
arXiv2023

Addition-deletion results for plus-one generated curves

In the recent paper A. Dimca proves that when one adds to or deletes a line from a free curve the resulting curve is either free or plus-one generated. We prove the converse statements, we give an additional insight into the original deletion result, and derive a characterisation of free curves in terms of behaviour to addition/deletion of lines. We describe the possible splitting types of the bundle of logarithmic vector fields associated to a plus-one generated curve.

math.AG↗