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Alba Larraya Sancho 2026-09-11 12:24:29 +02:00
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generaldegreeHypersurfaces.tex
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@ -61,9 +61,9 @@ MICIU/AEI/10.13039/501100011033 and CEX2021-001142-S-20-9.}
\begin{abstract} \begin{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. 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 $n$- dimensional $\Delta$-complex that is a strong deformation retract of the complement of a Fermat hypersurface of degree $d$ in the complex projective space of dimension $n$.
The retraction is performed in several steps, using the branched cover structure of the Fermat curves to the degree $1$ case. The retraction is performed in several steps, using the branched cover structure of the Fermat hypersurfaces to the degree $1$ case.
\end{abstract} \end{abstract}
\maketitle \maketitle