No. 6

This surface is part of a series of surfaces of degree d in Pn similar to the one introduced by Chmutov (cf. p. 419 in: Arnold et. al: Singularities of Differential Maps, Vol. II, 1988, Birkhäuser). It has real singularities of type Aj (for j=1 and most d and n this gives less nodes than Chmutov's original surfaces, but these are complex nodes). The image below for j=1, d=8 and n=3 is given by the affine equation:

(Td/2( x1 ))j+1 + (Td/2( x2 ))j+1 + (Td/2( x3 ))j+1 = 1,

where T4( xi ) = 8 xi4 - 8 xi2 + 1 denotes the Chebyshev polynomial of degree 4 with critical values +1,-1. It is an octic with 144 nodes. Contact me for more information.

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