A046001 Maximal number of ordinary double points on an n-th degree algebraic surface in complex projective 3-space.

0, 1, 4, 16, 31, 65

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

Table of n, a(n) for n=1..6.

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

Sequence in context: A366814 A031003 A324784 * A239611 A359195 A373077

Adjacent sequences: A045998 A045999 A046000 * A046002 A046003 A046004

Keyword

nonn,nice,hard,more

Author

Eric W. Weisstein

Status

approved