The eight types of rational double points (the type being the one excluded) can occur in only 20 combinations
on a cubic surface (of which Fischer 1986a gives
19): ,
,
,
,
,
,
,
,
,
,
,
,
,
(),
,
,
,
,
and
(Looijenga 1978, Bruce and Wall 1979, Fischer 1986a).
In particular, on a cubic surface, precisely those configurations of rational double points occur for which the disjoint 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 1986a).
Bruce, J. and Wall, C. T. C. "On the Classification of Cubic Surfaces." J. London Math. Soc.19, 245-256, 1979.Fischer,
G. (Ed.). Mathematische
Modelle aus den Sammlungen von Universitäten und Museen, Kommentarband.
Braunschweig, Germany: Vieweg, p. 13, 1986a.Fischer, G. (Ed.).
Plates 14-31 in Mathematische
Modelle aus den Sammlungen von Universitäten und Museen, Bildband. Braunschweig,
Germany: Vieweg, pp. 17-31, 1986b.Looijenga, E. "On the Semi-Universal
Deformation of a Simple Elliptic Hypersurface Singularity. Part II: The Discriminant."
Topology17, 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.
,
,
,
,
,
,
,
and 
).
type being the one excluded) can occur in only 20 combinations
on a cubic surface (of which Fischer 1986a gives
19): 
,
,
,
,
,
,
,
,
,
,
,
,
,
(
),
,
,
,
,
and 
(Looijenga 1978, Bruce and Wall 1979, Fischer 1986a).
. Also, a surface specializes to a more complicated one
precisely when its graph is contained in the graph of the other one (Fischer 1986a).
