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arXiv · 1511.06812

Vanishing polyhedron and collapsing map

Lê Dũng Tráng·Aurélio Menegon Neto
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Abstract

In this paper we give a detailed proof that the Milnor fiber $X_t$ of an analytic complex isolated singularity function defined on a reduced $n$-equidimensional analytic complex space $X$ is a regular neighborhood of a polyhedron $P_t \subset X_t$ of real dimension $n-1$. Moreover, we describe the degeneration of $X_t$ onto the special fiber $X_0$, by giving a continuous collapsing map $Ψ_t: X_t \to X_0$ which sends $P_t$ to $\{0\}$ and which restricts to a homeomorphism $X_t \backslash P_t \to X_0 \backslash \{0\}$.

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Lê Dũng Tráng, Aurélio Menegon Neto. 2015-11-21. Vanishing polyhedron and collapsing map. https://arxiv.org/abs/1511.06812

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