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arXiv · 2507.16374

Homotopy type of complements of fiber-type curves

José I. Cogolludo-Agustín·Eva Elduque
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Abstract

In this note we study the homotopy type of the complement of a plane projective curve of fiber-type. Roughly speaking, a curve of fiber-type is a finite union of fibers of a pencil. Under some restrictions, a full description of their homotopy type is given. In the context of fiber-type curves, we also partially answer in the positive a question originally posed by Libgober on the homotopy type of complements of plane curves, namely, whether or not the homotopy type of a curve complement is determined by the fundamental group and its Euler characteristic.

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José I. Cogolludo-Agustín, Eva Elduque. 2025-07-22. Homotopy type of complements of fiber-type curves. https://arxiv.org/abs/2507.16374

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