A minimal triangulation of complex projective plane admitting a chess colouring of four-dimensional simplices

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Abstract

We construct and study a new 15-vertex triangulation X of the complex projective plane ℂP2. The automorphism group of X is isomorphic to S4 × S3. We prove that the triangulation X is the minimal (with respect to the number of vertices) triangulation of ℂP2 admitting a chess colouring of four-dimensional simplices. We provide explicit parametrizations for the 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 find a 33-vertex subdivision X̄ of the triangulation X such that the classical moment mapping μ: ℂP2 → Δ2 is a simplicial mapping of the triangulation X̄ onto the barycentric subdivision of the triangle Δ2. We study the relationship of the triangulation X with complex crystallographic groups.

Original languageEnglish
Pages (from-to)29-48
Number of pages20
JournalProceedings of the Steklov Institute of Mathematics
Volume266
Issue number1
DOIs
Publication statusPublished - Oct 2009
Externally publishedYes

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