Journal of the
Korean Mathematical Society JKMS

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.

Keywords: plane curves, conic pencil, free curve, syzygy, Alexander polynomial

MSC numbers: Primary 14H50; Secondary 14B05, 13D02, 32S35, 32S40, 32S55