Introduction to Mixed Hypersurface Singularity

Mutsuo Oka ()
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Mutsuo Oka: Tokyo University of Science

Chapter Chapter 8 in Handbook of Geometry and Topology of Singularities II, 2021, pp 403-461 from Springer

Abstract: Abstract In 1968, Milnor introduced the fibration structure $$\varphi :\mathbb S_\varepsilon ^{2n-1}\setminus K\rightarrow \mathbb S^1$$ φ : S ε 2 n - 1 \ K → S 1 for a given holomorphic function $$f:(\mathbb C^n, \mathbf{0})\rightarrow (\mathbb C, 0)$$ f : ( C n , 0 ) → ( C , 0 ) where $$\varphi =f/|f|$$ φ = f / | f | and $$\varepsilon $$ ε is chosen small enough and $$K=f^{-1}(0)\cap \mathbb S_\varepsilon ^{2n-1}$$ K = f - 1 ( 0 ) ∩ S ε 2 n - 1 [24]. From a viewpoint of algebraic geometry, it is more convenient to study the tubular fibration $$f:E(\varepsilon , \delta )^*\rightarrow \mathbb D_\delta ^*$$ f : E ( ε , δ ) ∗ → D δ ∗ where $$E(\varepsilon , \delta )^*=\{\mathbf{z}\in \mathbb B_\varepsilon ^{2n}\, |\, 0

Date: 2021
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DOI: 10.1007/978-3-030-78024-1_8

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