A Minimal Triangulation of Complex Projective Plane Admitting a Chess Colouring of Four-dimensional Simplices
نویسنده
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.
منابع مشابه
Flag-transitive Point-primitive symmetric designs and three dimensional projective special linear groups
The main aim of this article is to study (v,k,λ)-symmetric designs admitting a flag-transitive and point-primitive automorphism group G whose socle is PSL(3,q). We indeed show that the only possible design satisfying these conditions is a Desarguesian projective plane PG(2,q) and G > PSL(3,q).
متن کاملOn a vertex-minimal triangulation of RP
We give three constructions of a vertex-minimal triangulation of 4-dimensional real projective space RP4. The first construction describes a 4-dimensional sphere on 32 vertices, which is a double cover of a triangulated RP4 and has a large amount of symmetry. The second and third constructions illustrate approaches to improving the known number of vertices needed to triangulate n-dimensional re...
متن کاملProof of a conjecture of Bowlin and Brin on four-colouring triangulations
We prove a conjecture of Bowlin and Brin that for all n ≥ 5, the n-vertex biwheel is the planar triangulation with n vertices admitting the largest number of four-colourings.
متن کاملComplexes of $C$-projective modules
Inspired by a recent work of Buchweitz and Flenner, we show that, for a semidualizing bimodule $C$, $C$--perfect complexes have the ability to detect when a ring is strongly regular.It is shown that there exists a class of modules which admit minimal resolutions of $C$--projective modules.
متن کاملSixteen-dimensional Locally Compact Translation Planes Admitting Sl2 H as a Group of Collineations
In this paper, all 16-dimensional locally compact translation planes admitting the unimodular quaternion group SL2H as a group of collineations will be determined explicitly. Besides the classical plane over the octonions there are a vast number of planes having this property, cf. the Classification Theorem (2.8). Indeed, the class of these planes covers an interesting borderline case: Among al...
متن کامل