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Titlebook: New Developments in Singularity Theory; D. Siersma,C. T. C. Wall,V. Zakalyukin Book 2001 Springer Science+Business Media Dordrecht 2001 Me

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NATO Science Series II: Mathematics, Physics and Chemistryhttp://image.papertrans.cn/n/image/665041.jpg
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https://doi.org/10.1007/978-94-010-0834-1Meromorphic function; Monodromy; Tensor; manifold; singularity theory
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978-0-7923-6997-4Springer Science+Business Media Dordrecht 2001
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Applications of Flag Contact Singularitieshe projections (wavefronts) of Legendre submanifolds of pro- jectivized cotangent bundles. Arnold’s list of simple classes (related to A,D,E Lie algebras) provides normal forms of generic wavefront singularities in small dimensions.
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Resolutions of discriminants and topology of their complements polynomials with multiple roots, . sets of polynomial systems having common roots, spaces of functions with degenerate singular points, of non-smooth algebraic varieties, of linear operators with zero or multiple eigenvalues, of smooth maps .. →.. (. ≥ 3) having singular or self-intersection points, of non-generic plane curves, and many others.
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The theory of integral closure of ideals and modules: Applications and new developmentss. The theory of the integral closure of ideals and modules provides a very useful tool for studying these limiting structures. In this paper we illustrate how these tools are used in three case studies, and describe some of the advances in the theory since the survey article of [.], which was written in 1996.
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