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arXiv · 2312.06792

Double points and image of reflection maps

Jose Rafael Borges Zampiva·Guillermo Penafort-Sanchis·Bruna Orefice-Okamoto·Joao Nivaldo Tomazella
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Abstract

A reflection mapping is a singular holomorphic mapping obtained by restricting the quotient mapping of a complex reflection group. We study the analytic structure of double point spaces of reflection mappings. In the case where the image is a hypersurface, we obtain explicit equations for the double point space and for the image as well. In the case of surfaces in $\C^3$, this gives a very efficient method to compute the Milnor number and delta invariant of the double point curve.

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Jose Rafael Borges Zampiva, Guillermo Penafort-Sanchis, Bruna Orefice-Okamoto, Joao Nivaldo Tomazella. 2023-12-11. Double points and image of reflection maps. https://arxiv.org/abs/2312.06792

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