A Minimal Triangulation of Complex Projective Plane Admitting a Chess Colouring of Four-dimensional Simplices

نویسنده

  • A. A. GAIFULLIN
چکیده

In this paper we construct and study a new 15-vertex triangulationX of the complex projective plane CP. The automorphism group of X is isomorphic to S4 ×S3. We prove that the triangulation X is the minimal by the number of vertices triangulation of CP admitting a chess colouring of four-dimensional simplices. We provide explicit parametrizations for simplices of X and show that the automorphism group of X can be realized as a group of isometries of the Fubini–Study metric. We provide a 33-vertex subdivision X of the triangulation X such that the classical moment mapping μ : CP → ∆ is a simplicial mapping of the triangulation X onto the barycentric subdivision of the triangle ∆. We study the relationship of the triangulation X with complex crystallographic groups.

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تاریخ انتشار 2009