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A046001 Maximal number of ordinary double points on an n-th degree algebraic surface in complex projective 3-space. 0
0, 1, 4, 16, 31, 65 (list; graph; refs; listen; history; text; internal format)
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

REFERENCES

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

LINKS

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

S. Endrass, Surfaces with many ordinary nodes

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: A173019 A031003 A324784 * A239611 A031050 A243980

Adjacent sequences:  A045998 A045999 A046000 * A046002 A046003 A046004

KEYWORD

nonn,nice,hard

AUTHOR

Eric W. Weisstein

STATUS

approved

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Last modified November 14 02:19 EST 2019. Contains 329108 sequences. (Running on oeis4.)