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- W225611938 abstract "We shall consider normal surface Gorenstein singularities. Let (V, p) be a normal surface singularity, i.e., V is a two-dimensional normal analytic space and p is its only singular point. If there exist an open neighborhood U of p in V and a non-vanishing holomorphic 2-form on the deleted neighborhood U-{p}, then we say that (V, p) is a Gorenstein singularity. Gazing on known results of classifications of singularities, we may sometimes meet with new general properties for singularities. It seems that such expectation is not a regular tactics for attack, but at least, that may be a clue to discovery, or a judgement for a conjecture. Quasihomogeneous hypersurface isolated singularities are easy examples to deal with,I think so. Indeed, their minimal good, or minimal resolutions' weighted dual graphs will be calculated with Orlik-Wagreich's method [6], or Laufer's one [3], and almost all their invariants will be calculated from their weights (quasihomogeneous types of their defining functions) [7]. All those quasihomogeneous hypersurface isolated singularities whose geometric genera p, are less than, or equal to two have been classified. Quasihomogeneous hypersurface isolated singularities of p,=O are the Rational-Double-Points [2]; A., D., E6, E7 and Es. Quaihomogeneous hypersurface isolated singularities of P.==1 were classified into 45 types. Some of them are called simple elliptic singularities, and some of them are called the 14 exceptional singuiarities. Quasihomogeneous hypersurface isolated singularities of p,=2 were classified into 72-types [9]. In this paper, we shall decide all those quasihomogeneous types which give p,=3. Normal surface Gorenstein singularities of P,==2 are weakly elliptic, so possible weighted dual graphs of their resolutions are topologically restricted. But, in case of p,==3, such restriction is not held. So if we want to find general properties among non-weakly elliptic Gorenstein singularities of p.lll3, then our classification will be of use for some reason." @default.
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- W225611938 date "1981-11-01" @default.
- W225611938 modified "2023-09-23" @default.
- W225611938 title "Two-Dimensional Quasihomogeneous Singularities of p_g=3" @default.
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