Vanishing polyhedron and collapsing map
| Autor: | Lê Dũng Tráng, Aurélio Menegon Neto |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: |
Statistics::Theory
Fiber (mathematics) Mathematics - Complex Variables General Mathematics 010102 general mathematics Function (mathematics) Complex dimension Isolated singularity 01 natural sciences Combinatorics 010104 statistics & probability Polyhedron Complex space Mathematics::Probability Homeomorphism (graph theory) Backslash 0101 mathematics Mathematics |
| Popis: | In this paper we give a detailed proof of the fact 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 $$\psi _t: X_t \rightarrow X_0$$ which sends $$P_t$$ to $$\{0\}$$ and which restricts to a homeomorphism $$X_t {\backslash } P_t \rightarrow X_0 {\backslash } \{0\}$$ . |
| Databáze: | OpenAIRE |
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