Sphericity of a real hypersurface via projective geometry

2015/10/12 by Kossovskiy, Ilya
#Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1510.03323

Abstract

In this work, we obtain an unexpected geometric characterization of sphericity of a real-analytic Levi-nondegenerate hypersurface M⊂\mathbb C². We prove that M is spherical if and only if its Segre (-Webster) varieties satisfy an elementary combinatorial property, identical to a property of straight lines on the plane and known in Projective Geometry as the \em Desargues Theorem.

Related

• On the real-analyticity of rigid spherical hypersurfaces in mathbb\n C²
• Nonrigid spherical real analytic hypersurfaces in C²
• Extremal discs and Segre varieties for real-analytic hypersurfaces in ℂ²
• Sphericity and Analyticity of a strictly pdeusoconvex hypersurface in low regularity I
• On Segre-degenerate Levi-flat hypervarieties