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Surfaces with many ordinary double points

A surface X={f=0} in complex projective threespace P3(C) admits at most finitely many ordinary double points (nodes). The maximum number is denoted by µ(d) and depends on the degree d=deg(X)=deg(f) of the surface. The numbers µ(d) are known for d<7:

d 123456
µ(d) 014163165

For d>6 we have estimates:

d 789101112->oo
µ(d)>= 931682163453756005/12 d ³
µ(d)<= 1041742463604806454/9 d ³

Have a look at some examples for d>=3:

Stephan Endraß
Last update: Thursday, 06-Feb-2003 08:53:51 CET

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