A301894 Number of real lines on a smooth real cubic surface.

3, 7, 15, 27

Offset

1,1

Comments

Schläfli proved that a smooth real cubic surface contains either 3, 7, 15, or 27 straight lines.

Links

Table of n, a(n) for n=1..4.

D. Schläfli, On the distribution of surfaces of the third order into species, in reference to the absence or presence of singular points, and the reality of their lines, Philosophical Transactions of the Royal Society of London, 153 (1863), 193-241.

Kirsten Wickelgren, An Arithmetic Count of the Lines on a Smooth Cubic Surface, AMS Notices, 65 (2018), 404-405.

Formula

a(n) = A097080(n) = 2*n^2 - 2*n + 3 for n = 1, 2, 3, 4.

Example

The number of lines on a smooth complex cubic surface is a(4) = A027363(2) = A238370(1) = 27.

Crossrefs

Cf. A027363, A238370.

Sequence in context: A051054 A001649 A303220 * A213215 A353578 A324719

Adjacent sequences: A301891 A301892 A301893 * A301895 A301896 A301897

Keyword

nonn,fini,full

Author

Jonathan Sondow, Mar 28 2018

Status

approved