# Free and nearly free curves from conic pencils

## TL;DR

This paper constructs infinite series of free and nearly free algebraic curves using conic pencils, analyzing their topology, Alexander polynomial, Milnor fibers, and monodromy eigenspaces, revealing new insights into their geometric and topological properties.

## Contribution

It introduces a novel method to generate free and nearly free curves from conic pencils and explicitly studies their topological invariants and monodromy characteristics.

## Key findings

- High degree Alexander polynomial explicitly determined
- Milnor fiber homotopy equivalent to a bouquet of circles
- Irreducible translated component in the characteristic variety

## Abstract

We construct some infinite series of free and nearly free curves using pencils of conics with a base locus of cardinality at most two. These curves have an interesting topology, e.g. a high degree Alexander polynomial that can be explicitly determined, a Milnor fiber homotopy equivalent to a bouquet of circles, or an irreducible translated component in the characteristic variety of their complement. Monodromy eigenspaces in the first cohomology group of the corresponding Milnor fibers are also described in terms of explicit differential forms.