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Global study of webs on a holomorphic surface. (Introduction à l’étude globale des tissus sur une surface holomorphe.) (French. English summary) Zbl 1129.14015
In this paper, the authors study how to globalize the existing local notions on webs (near a regular point). They define tools for a global study of webs on a holomorphic surface. After two preliminary and introductory sections, this is made in Section 3 of the paper, where new concepts, like type, dicriticity, indistinguishability or quasi-smoothness appear. Notice that these concepts have no interest in the local case near a regular point. The case when the surface is the projective plane is treated in Section 4. Finally, in Section 6 is given a global definition of the space of abelian relations for a web that is suitable to benefit from the results and applications of a paper by A. Hénaut [Ann. Math. 159, 425–445 (2004; Zbl 1069.53020)].

14C21 Pencils, nets, webs in algebraic geometry
53A60 Differential geometry of webs
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