On four-dimensional terminal quotient singularities

Mori, Shigefumi; Morrison, David R.; Morrison, Ian

doi:10.1090/S0025-5718-1988-0958643-5

On four-dimensional terminal quotient singularities
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by Shigefumi Mori, David R. Morrison and Ian Morrison PDF

Math. Comp. 51 (1988), 769-786 Request permission

Abstract:

We report on an investigation of four-dimensional terminal cyclic quotient singularities which are not Gorenstein. (For simplicity, we focus on quotients by cyclic groups of prime order.) An enumeration, using a computer, of all such singularities for primes $< 1600$ led us to conjecture a structure theorem for these singularities (which is rather more complicated than the known structure theorem in dimension three). We discuss this conjecture and our evidence for it; we also discuss properties of the anticanonical and antibicanonical linear systems of these singularities.

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