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Retraction of the complement of smooth projective hypersurfaces to an n-dimensional Δ-complex
Abstract
We give an explicit strong deformation retraction of the complement of a Fermat hypersurface of degree d in the complex projective space of dimension n into a Δ-complex of real dimension~n. This retraction is performed in several steps, using the branched cover structure of the Fermat hypersurfaces to the degree $1$ case. Moreover, an implementation of the method in \texttt{Sagemath} is provided.
Related
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BibTeX
@misc{artal2026retraction,
title = {{Retraction of the complement of smooth projective hypersurfaces to an $n$-dimensional $Δ$-complex}},
author = {E. Artal and A. Larraya Sancho and M. A. Marco Buzunariz},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.26768},
eprint = {2605.26768},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.26768},
}
RIS
TY - UNPB
TI - Retraction of the complement of smooth projective hypersurfaces to an n-dimensional Δ-complex
AU - E. Artal
AU - A. Larraya Sancho
AU - M. A. Marco Buzunariz
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2605.26768
UR - https://arxiv.org/abs/2605.26768
AB - We give an explicit strong deformation retraction of the complement of a Fermat hypersurface of degree d in the complex projective space of dimension n into a Δ-complex of real dimension~n. This retraction is performed in several steps, using the branched cover structure of the Fermat hypersurfaces to the degree $1$ case. Moreover, an implementation of the method in \texttt{Sagemath} is provided.
ER -