The surfaces V(x1^a1 + x2^a2 + x3^a3 + 1 = 0) and V(y1^b1 + y2^b2 + y3^b3 + 1 = 0) are isomorphic over C if and only if the exponent tuples are permutations of each other.
arXiv preprint arXiv:2306.00510 , year=
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The Isomorphism Classes of the Surfaces $x_1^{a_1} + x_2^{a_2} + x_3^{a_3} + 1 = 0$
The surfaces V(x1^a1 + x2^a2 + x3^a3 + 1 = 0) and V(y1^b1 + y2^b2 + y3^b3 + 1 = 0) are isomorphic over C if and only if the exponent tuples are permutations of each other.