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Tr. Mat. Inst. Steklova, 2009, Volume 266, Pages 33–53 (Mi tm1871)  

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

A. A. Gaifullinab

a Moscow State University, Moscow, Russia
b Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia

Abstract: We construct and study a new 15-vertex triangulation $X$ of the complex projective plane $\mathbb C\mathrm P^2$. The automorphism group of $X$ is isomorphic to $S_4\times S_3$. We prove that the triangulation $X$ is the minimal (with respect to the number of vertices) triangulation of $\mathbb C\mathrm P^2$ 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 $\overline X$ of the triangulation $X$ such that the classical moment mapping $\mu\colon\mathbb C\mathrm P^2\to\Delta^2$ is a simplicial mapping of the triangulation $\overline X$ onto the barycentric subdivision of the triangle $\Delta^2$. We study the relationship of the triangulation $X$ with complex crystallographic groups.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2009, 266, 29–48

Bibliographic databases:

UDC: 515.142.33
Received in April 2009

Citation: A. A. Gaifullin, “A Minimal Triangulation of Complex Projective Plane Admitting a Chess Colouring of Four-Dimensional Simplices”, Geometry, topology, and mathematical physics. II, Collected papers. Dedicated to Academician Sergei Petrovich Novikov on the occasion of his 70th birthday, Tr. Mat. Inst. Steklova, 266, MAIK Nauka/Interperiodica, Moscow, 2009, 33–53; Proc. Steklov Inst. Math., 266 (2009), 29–48

Citation in format AMSBIB
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\paper A Minimal Triangulation of Complex Projective Plane Admitting a~Chess Colouring of Four-Dimensional Simplices
\inbook Geometry, topology, and mathematical physics.~II
\bookinfo Collected papers. Dedicated to Academician Sergei Petrovich Novikov on the occasion of his 70th birthday
\serial Tr. Mat. Inst. Steklova
\yr 2009
\vol 266
\pages 33--53
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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