What does this research mean for the field?

The position of nodes affects the topology of the embedding of projective curves, as demonstrated by the existence of an infinite family of Zariski pairs of fiber-type curves whose complements have non-isomorphic fundamental groups. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

This research investigates conditions under which curves in projective surfaces have specific fundamental groups related to their complements.

April 10, 2026Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A MatemáticasOpen Access

On the topology of fiber-type curves: an affine Zariski pair of nodal curves

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This research investigates conditions under which curves in projective surfaces have specific fundamental groups related to their complements.
Examine properties of curves in the projective surface P^2.
Identify an infinite family of Zariski pairs among fiber-type curves.
Utilize twisted Alexander polynomials to analyze fundamental groups.
Demonstrated pairs of fiber-type curves with homeomorphic tubular neighborhoods but differing embeddings in P^2.
Identified non-isomorphic fundamental groups within an example of curves in C^2, with one being free.
Showed that the arrangement of nodes influences the topology of projective curve embeddings.

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Implication

Exploration of nodal curves and their topology, revealing relationships between embeddings and their complements.

Cite This Study

Cogolludo-Agustín et al. (2026) studied this question.

synapsesocial.com/papers/69d8970c6c1944d70ce08425 https://doi.org/10.1007/s13398-026-01853-1

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On the topology of fiber-type curves: an affine Zariski pair of nodal curves

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Cite This Study

On the topology of fiber-type curves: an affine Zariski pair of nodal curves

Key Points

Discussion

Implication

Cite This Study

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