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Titlebook: Holomorphic Foliations with Singularities; Key Concepts and Mod Bruno Scárdua Textbook 2021 The Editor(s) (if applicable) and The Author(s)

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The Classical Notions of Foliations,This chapter is intended to introduce the classical notions of foliation in the real framework. There- fore, smooth foliations are introduced as well as the correlate main concept of holonomy. The reader which is already familiar with these notions may skip to the next chapter.
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Holomorphic Foliations: Non-singular Case,In this chapter we introduce and discuss the concept of holomorphic foliation in the non-singular case. Basic constructions and examples are presented and we also motivate the forthcoming notion of holomorphic foliation with singularities.
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Holomorphic Foliations with Singularities,In this chapter we introduce the concept of holomorphic foliation with singularities, focusing on the two cases: dimension one and codimension one.
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Foliations with Algebraic Limit Sets,In this chapter we introduce and study the notion of limit set of a holomorphic foliation with singularities. We focus on the case of foliations on the complex projective plane having a limit set which is assumed to be algebraic of dimension one.
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Some Modern Questions,This chapter is devoted to some more recent developments and problems in the theory of holomorphic foliations with singularities. We present a non-exhaustive list of subjects of current interest and some results that were recently obtained.
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