“Godeaux surface”的意思、由来-开放百科全书

词条

Godeaux surface

释义

Construction
Invariants
See also
References

In mathematics, a Godeaux surface is one of the surfaces of general type introduced by Lucien Godeaux in 1931.

Other surfaces constructed in a similar way with the same Hodge numbers are also sometimes called Godeaux surfaces. Surfaces with the same Hodge numbers (such as Barlow surfaces) are called numerical Godeaux surfaces.

Construction

The cyclic group of order 5 acts freely on the Fermat surface of points (w : x : y : z)

in P³ satisfying w⁵ + x⁵ + y⁵ + z⁵ = 0 by mapping (w : x : y : z) to (w:ρx:ρ²y:ρ³z) where ρ is a fifth root of 1. The quotient by this action is the original Godeaux surface.

Invariants

The fundamental group (of the original Godeaux surface) is cyclic of order 5.

It has invariants like rational surfaces do, though it is not rational. The square of the first Chern class (and moreover the canonical class is ample).

{{Hodge diamond|style=font-weight:bold
| caption = Hodge diamond
| 1
| 0 | 0
| 0 | 9 | 0
| 0 | 0
| 1
}}

References

{{Citation | last1=Barth | first1=Wolf P. | last2=Hulek | first2=Klaus | last3=Peters | first3=Chris A.M. | last4=Van de Ven | first4=Antonius | title=Compact Complex Surfaces | publisher= Springer-Verlag, Berlin | series=Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. | isbn=978-3-540-00832-3 |mr=2030225 | year=2004 | volume=4}}

2 : Algebraic surfaces|Complex surfaces

随便看

开放百科全书收录14589846条英语、德语、日语等多语种百科知识，基本涵盖了大多数领域的百科知识，是一部内容自由、开放的电子版国际百科全书。

Construction

Invariants

See also

References