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

S. Endrass, Surfaces with many ordinary nodes

S. Endrass, Flaechen mit vielen Doppelpunkten DMV-Mitteilungen 4 (April 1995), 17-20.

Soliver Labs, A septic with 99 real nodes, arXiv:math/0409348 [math.AG] (2004).

Oliver Labs, Nodal surfaces

Eric Weisstein's World of Mathematics, Ordinary Double Point

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