We study the miniversal deformations of minimally elliptic two-dimensional singularities of multiplicities of $5$, $6$ and $7$. By restricting the miniversal deformations on the line transverse to the discriminant locus, we construct many new three-dimensional isolated rational Gorenstein singularities with one-dimensional equisingular deformation and nontrivial $T^2$. In fact the three-dimensional isolated rational Gorenstein singularities constructed from minimally elliptic singularities of multiplicity $5$ has four-dimensional family of deformation, of which one-dimensional family is equisingular in the sense of Hilbert polynomial. On the other hand, the three-dimensional isolated rational Gorenstein singularities constructed from minimally elliptic singularities of multiplicity $6$ and $7$ respectively has nontrivial $T^2$ and has one-dimensional equisingular family of deformation. These singularities define many new interesting four dimensional $N = 2$ superconformal field theories.

中文翻译：

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$ 4d $ $ N = 2 $ SCFT和奇点理论第四部分：具有至少一维变形和非平凡的$ T ^ 2 $的孤立有理Gorenstein非完全交点奇点

我们研究了多重椭圆的$ 5 $，$ 6 $和$ 7 $的最小椭圆二维奇点的极小变形。通过限制横向于判别轨迹的线上的微小变形，我们构造了许多新的具有一维等值变形和非平凡的$ T ^ 2 $的三维孤立的有理Gorenstein奇异点。实际上，由多重性$ 5 $的最小椭圆奇异点构成的三维孤立有理Gorenstein奇点具有变形的四维族，其中一维族在希尔伯特多项式意义上是等奇的。另一方面，由分别由多重性$ 6 $和$ 7 $组成的最小椭圆奇异性构造的三维孤立有理Gorenstein奇异性具有非平凡的TT ^ 2 $且具有一维等式形变族。这些奇异性定义了许多新的有趣的二维$ N = 2 $超保形场论。