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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
LINKS
S. Endrass, Flaechen mit vielen Doppelpunkten DMV-Mitteilungen 4 (April 1995), 17-20.
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 A031050
KEYWORD
nonn,nice,hard,more
AUTHOR
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)