Let
(or 
) be a space curve. Then a point 
(where 
denotes the immersion of f) is an ordinary double point if its preimage under f consists of two values 
and 
, and the two tangent vectors 
and 
are noncollinear. Geometrically, this means that, in a neighborhood of p, the curve consists of two transverse branches. Ordinary double points are isolated singularities having Coxeter-Dynkin diagram of type 
, and also called "nodes" or "simple double points." 
The above plot shows the curve
, which has an ordinary double point at the origin.A surface in complex three-space admits at most finitely many ordinary double points. The maximum possible number of ordinary double points
for a surface of degree d = 1,2, ..., are 0, 1, 4, 16, 31, 65,
,
,
,
,
,
... (Sloane's A046001;Chmutov 1992, Endraß 1995).
was known to Kummer in 1864 (Chmutov 1992), the fact that 
was proved by Beauville (1980), and 
was proved by Jaffe and Ruberman (1994). For 
, the following inequality holds:
(Endraß 1995). Examples of algebraic surfaces having the maximum (known) number of ordinary double points are given in the following table.
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