论文标题
从其模量代数重建超表面奇异性
Reconstruction of a Hypersurface Singularity from its Moduli Algebra
论文作者
论文摘要
在本文中，我们提出了一种建设性的方法来表征本地环$ \ Mathscr {o} _ {\ Mathbb {\ Mathbb {C}^n，0} $ holomorphic函数的细菌$ 0 \ in \ Mathbb {C}^n $，这是MATHBB {C}^n $，这是Moduli Ideal $ \ langle f，\ langle f，\ langle f，\ rang。 j（f）\ rangle $，对于某些$ f \ in \ mathfrak {m} \ subset \ mathscr {o} _ {\ mathbb {c}^n，0} $。我们表征的结果是一种可以追溯到1980年代的问题的有效解决方案，称为其模量代数的超表面奇异性的重建问题。我们的结果起作用，无论超出表面奇异性是孤立的。
In this paper we present a constructive method to characterize ideals of the local ring $\mathscr{O}_{\mathbb{C}^n,0}$ of germs of holomorphic functions at $0\in\mathbb{C}^n$ which arise as the moduli ideal $\langle f,\mathfrak{m}\, j(f)\rangle$, for some $f\in\mathfrak{m}\subset\mathscr{O}_{\mathbb{C}^n,0}$. A consequence of our characterization is an effective solution to a problem dating back to the 1980's, called the Reconstruction Problem of the hypersurface singularity from its moduli algebra. Our results work regardless of whether the hypersurface singularity is isolated or not.
