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On surfaces and their contours

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Abstract

We prove two theorems concerning the global behaviour of a smooth compact surfaceS, without boundary, embedded in a real projective space or mapped to a plane. Our starting point is an analysis of the orientability properties of the normal bundle of a singular projective curve. Then we see how an excellent projection fromS to the Euclidean plane gives rise to integral relations linking the singularities of the apparent contour. Finally, given an embedding ofS in RPn, we look at the discriminant Δ* of a net of hyperplanes that intersectsS in a generic way, obtaining a characterization of Δ* in terms of mod.2 cohomology invariants.

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  1. Dip. di Matematica “Federigo Enriques”, Università di Milano, Via C.Saldini n.50, 20133, Milano, Italia

    Roberto Pignoni

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  1. Roberto Pignoni
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Pignoni, R. On surfaces and their contours. Manuscripta Math 72, 223–249 (1991). https://doi.org/10.1007/BF02568277

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  • DOI: https://doi.org/10.1007/BF02568277

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