A207540 Degrees (with multiplicity) of simple surface singularities (ADE singularities, Du Val singularities, double rational points, Gorenstein quotient singularities, Klein singularities).

2, 4, 6, 6, 6, 8, 8, 10, 10, 10, 12, 12, 12, 14, 14, 14, 16, 16, 18, 18, 18, 18, 20, 20, 22, 22, 22, 24, 24, 26, 26, 26, 28, 28, 30, 30, 30, 30

Offset

1,1

Comments

Adapted from Table 3, p. 46, Dolgachev.

Links

Table of n, a(n) for n=1..38.

Igor V. Dolgachev, Reflection groups in algebraic geometry, Bull. Amer. Math. Soc. 45 (2008), 1-60.

Formula

With multiplicity: {4k+2, k => 1} and {2k+2, k => 0} and {2n-2, n => 4} and {12, 18, 30}.

Example

(6, 6, 6) because 4*1 + 2 = 6 (corresponding to isomorphism class A_4), 2*2 + 2 = 6 (corresponding to isomorphism class A_5), 2*4 - 2 = 6 (corresponding to isomorphism class D_4).
The greatest element in this sequence with multiplicity 4 is 30, corresponding to the sporadic E_8.

Crossrefs

Sequence in context: A296511 A050823 A209863 * A050825 A174342 A111150

Adjacent sequences: A207537 A207538 A207539 * A207541 A207542 A207543

Keyword

nonn

Author

Jonathan Vos Post, Feb 18 2012

Status

approved