AI 中文总结
该研究对一大类次数证明三维点希尔伯特概型极大奇异性的必要条件猜想，推广了相关结果并为该领域提供了新的切空间维数分析方法。
AI 中文摘要
我们对一大类次数证明了三维空间中点的希尔伯特概型的极大奇异性的必要条件猜想（[27, 猜想B]），这特别意味着四面体次数下的1978年Briançon-Iarrobino猜想，并极大推广了[19]中的结果。该工作的创新之处在于：对所声称的非极大奇异理想的切空间维数引入新的上界，构造满足所声称的极大奇异性条件的典范理想，给出其切空间维数的下界，最后对两种情况进行比较。
英文摘要
We prove a necessary condition conjecture ([27, Conjecture B]) for the maximal singularity of the Hilbert scheme of points in 3D for a large class of degrees, which in particular implies the 1978 Briançon-Iarrobino Conjecture for a tetrahedral degree, and vastly generalises the result in [19]. The novelty lies in introducing a new upper bound on the dimensions of the tangent spaces of the claimed non-maximally singular ideals, constructing canonical ideals that satisfy the claimed maximal singularity condition, providing a lower bound on the dimension of their tangent spaces, and finally comparing the two cases.
Comments18 pages, 12 figures, comments welcome!
