RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Guidelines for authors License agreement Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Trudy MIAN: Year: Volume: Issue: Page: Find

 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.

Full text: PDF file (319 kB)
References: PDF file   HTML file

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
\Bibitem{Gai09} \by A.~A.~Gaifullin \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 \mathnet{http://mi.mathnet.ru/tm1871} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2603259} \zmath{https://zbmath.org/?q=an:1185.57019} \elib{http://elibrary.ru/item.asp?id=12901676} \transl \jour Proc. Steklov Inst. Math. \yr 2009 \vol 266 \pages 29--48 \crossref{https://doi.org/10.1134/S008154380903002X} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000270722100002} \elib{http://elibrary.ru/item.asp?id=15307868} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-70350400398}