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Characteristic Points, Fundamental Cubic Form and Euler Characteristic of Projective Surfaces

Abstract : We define local indices for projective umbilics and godrons (also called cusps of Gauss) on generic smooth surfaces in projective 3-space. By means of these indices, we provide formulas that relate the algebraic numbers of those characteristic points on a surface (and on domains of the surface) with the Euler characteristic of that surface (resp. of those domains). These relations determine the possible coexis-tences of projective umbilics and godrons on the surface. Our study is based on a "fundamental cubic form" for which we provide a simple closed expression.
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Maxim Kazarian, Ricardo Uribe-Vargas. Characteristic Points, Fundamental Cubic Form and Euler Characteristic of Projective Surfaces. Moscow Mathematical Journal, Independent University of Moscow 2020, 20 (3), pp.511-530. ⟨10.17323/1609-4514-2020-20-3-511-530⟩. ⟨hal-02568225v2⟩

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