On the topology of fibered-type curves: a Zariski pair of affine nodal curves

Author:

José Ignacio Cogolludo-Agustín, Eva Elduque

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG), Geometric Topology (math.GT)

journal:

date:

2023-06-11 16:00:00

Abstract

In this paper we explore conditions for the complement of a fibered-type curve to be a free product of cyclic groups. We exhibit a Zariski pair of curves in $\mathbb{C}^2$ with only nodes as singularities (and the same singularities at infinity) whose complements have non-isomorphic fundamental groups, one of them being free. This shows that the position of singularities also affects this problem and hence the sufficient conditions involve more than local invariants. We also study the homotopy type of projective curve complements whose fundamental groups are free products of cyclic groups. Finally we describe the CW-complex structure of certain fibered-type curve complements.

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