|
|
A046001
|
|
Maximal number of ordinary double points on an n-th degree algebraic surface in complex projective 3-space.
|
|
0
|
|
|
|
OFFSET
|
1,3
|
|
COMMENTS
|
For n >= 7 lower bounds are 99, 168, 226, 345, 425, 600, 732, 949; upper bounds are 104, 174, 246, 360, 480, 645, 829, 1051. The bounds on mu(d), the maximum number of singularities on a surface of degree d in three-space, are 5/12*d^3 <= mu(d) <= 4/9*d^3. - Corrected and extended by Martin Renner, Nov 10 2014
|
|
LINKS
|
|
|
EXAMPLE
|
For n = 3 there is a unique surface of degree 3 with 4 double points, Cayley's cubic: 4(w^3+x^3+y^3+z^3) = (w+x+y+z)^3.
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,nice,hard,more
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|