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arXiv · 2605.26768

Retraction of the complement of smooth projective curves to a $2$-dimensional $\Delta$-complex

E. Artal·A. Larraya Sancho·M. A. Marco Buzunariz
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Abstract

Due to a result by Andreotti and Frankel \cite{andreotti1959}, it can be seen that the complement of a complex projective curve has the homotopy type of a $2$-dimensional CW complex. However, no general method has been given to compute explicitly this complex. Here we give a explicit construction of a $2$- dimensional $\Delta$-complex that is a strong deformation retract of the complement of a Fermat curve of degree $d$ in the complex projective space. The retraction is performed in several steps, using the branched cover structure of the Fermat curves over the degree $1$ case.

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E. Artal, A. Larraya Sancho, M. A. Marco Buzunariz. 2026-05-26. Retraction of the complement of smooth projective curves to a $2$-dimensional $\Delta$-complex. https://arxiv.org/abs/2605.26768

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