“Rational Double Point”的概念、定义、习题解题方法及翻译-数学辞典

单词

Rational Double Point

释义

Rational Double Point

There are nine possible types of Isolated Singularities on a Cubic Surface, eight ofthem rational double points. Each type of Isolated Singularity has an associated normal form and Coxeter-DynkinDiagram (, , , , , , , and ).

The eight types of rational double points (the type being the one excluded) can occur in only 20 combinations ona Cubic Surface (of which Fischer 1986 gives 19): , , , , , , , , , , , , , (), , , , , and (Looijenga 1978, Bruce and Wall 1979, Fischer 1986).

In particular, on a Cubic Surface, precisely those configurations of rational double points occur for which thedisjoint union of the Coxeter-Dynkin Diagram is a Subgraph of the Coxeter-Dynkin Diagram . Also, a surface specializes to a more complicated one precisely when its graph is contained in the graph of the other one(Fischer 1986).

See also Coxeter-Dynkin Diagram, Cubic Surface, Isolated Singularity

References

Bruce, J. and Wall, C. T. C. ``On the Classification of Cubic Surfaces.'' J. London Math. Soc. 19, 245-256, 1979.

Fischer, G. (Ed.). Mathematical Models from the Collections of Universities and Museums. Braunschweig, Germany: Vieweg, p. 13, 1986.

Fischer, G. (Ed.). Plates 14-31 in Mathematische Modelle/Mathematical Models, Bildband/Photograph Volume. Braunschweig, Germany: Vieweg, pp. 17-31, 1986.

Looijenga, E. ``On the Semi-Universal Deformation of a Simple Elliptic Hypersurface Singularity. Part II: The Discriminant.'' Topology 17, 23-40, 1978.

Rodenberg, C. ``Modelle von Flächen dritter Ordnung.'' In Mathematische Abhandlungen aus dem Verlage Mathematischer Modelle von Martin Schilling. Halle a. S., 1904.

随便看

数学辞典收录了8975条数学词条，基本涵盖了常用数学知识及数学英语单词词组的翻译及用法，是数学学习的有利工具。