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Degrees (with multiplicity) of simple surface singularities (ADE singularities, Du Val singularities, double rational points, Gorenstein quotient singularities, Klein singularities).
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%I #10 Feb 13 2020 16:00:30

%S 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,

%T 22,22,24,24,26,26,26,28,28,30,30,30,30

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

%C Adapted from Table 3, p. 46, Dolgachev.

%H Igor V. Dolgachev, <a href="https://doi.org/10.1090/S0273-0979-07-01190-1">Reflection groups in algebraic geometry</a>, Bull. Amer. Math. Soc. 45 (2008), 1-60.

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

%e (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).

%e The greatest element in this sequence with multiplicity 4 is 30, corresponding to the sporadic E_8.

%K nonn

%O 1,1

%A _Jonathan Vos Post_, Feb 18 2012