## Abstract

We construct and study a new 15-vertex triangulation X of the complex projective plane ℂP^{2}. The automorphism group of X is isomorphic to S_{4} × S_{3}. We prove that the triangulation X is the minimal (with respect to the number of vertices) triangulation of ℂP^{2} 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: ℂP^{2} → Δ^{2} is a simplicial mapping of the triangulation X̄ onto the barycentric subdivision of the triangle Δ^{2}. We study the relationship of the triangulation X with complex crystallographic groups.

Original language | English |
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Pages (from-to) | 29-48 |

Number of pages | 20 |

Journal | Proceedings of the Steklov Institute of Mathematics |

Volume | 266 |

Issue number | 1 |

DOIs | |

Publication status | Published - Oct 2009 |

Externally published | Yes |