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

Результат исследований: Вклад в журналСтатьярецензирование

Аннотация

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.

Язык оригиналаАнглийский
Страницы (с-по)29-48
Число страниц20
ЖурналProceedings of the Steklov Institute of Mathematics
Том266
Номер выпуска1
DOI
СостояниеОпубликовано - окт. 2009
Опубликовано для внешнего пользованияДа

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