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Rigid flat web on the projective plane. (English) Zbl 1330.53020

The paper is devoted to the global classification of flat complex \(k\)-webs given on the projective plane by a \(k\)-symmetric polynomial 1-form (the local classification is trivial). The authors introduce the notion of reduced convex foliation and prove that the Legendre transform of reduced convex foliations are webs with zero curvature. This approach gives a possibility to point out a countably infinite family of convex foliations which gives rise to a family of webs with zero curvature not admitting any non-trivial deformations.

MSC:

53A60 Differential geometry of webs
14C21 Pencils, nets, webs in algebraic geometry
32S65 Singularities of holomorphic vector fields and foliations
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