Images of analytic map germs, and singular fibrations

Abstract

For a map germ $G$ with target $({\mathbb{C}}^p,0)$ or $({\mathbb{R}}^p,0)$ with $p\ge 2$, we address two phenomena which do not occur when $p=1$: the image of $G$ may be not well-defined as a set germ, and a local fibration near the origin may not exist. We show how these two phenomena are related, and how they can be characterised.

arXiv commentrevised, to appear in Europ. J. Math

References in corpus (9)

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• Regularity at infinity of real mappings and a Morse-Sard theorem
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• The Zariski-Lefschetz principle for higher homotopy groups of nongeneric pencils
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• Images of analytic map germs, and singular fibrations
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Cited by in corpus (10)

• Images of analytic map germs, and singular fibrations
• Milnor-Hamm sphere fibrations and the equivalence problem
• The vanishing cohomology of non-isolated hypersurface singularities
• On singular maps with local fibration
• Fibrations of tamely composable maps
• Milnor Fiber Consistency via Flatness
• Deformations with fibre constancy
• Some remarks about $\rho$-regularity for real analytic maps
• The local image problem for complex analytic maps
• Tame deformations of highly singular function germs