论文标题
关于超表面奇点的tjurina理想
On Tjurina Ideals of Hypersurface Singularities
论文作者
论文摘要
tjurina的helomorphic函数$ f $的tjurina理想是$ \ mathscr {o} _ {\ mathbbm {c}^n，0} $的理想 - 这些细菌的环为$ 0 \ in \ mathbbm {c}^n $ in $ f $ f $ in $ f $ in $ f $ in $ f $ int $ f $ and poptial and partial andial derivivestives。在这里，它用$ t（f）$表示。理想的$ t（f）$将封闭的亚cheme的结构（\ mathbbm {c}^n，0）$授予由$ f $定义的高表情奇异性，这是奇异理论中心兴趣的对象。在本说明中，我们介绍了\ emph {$ t $ - fullness}和\ emph {$ t $ - 依赖性}，这是两个易于验证的属性，以构成全体形态函数细菌的任意理想。这两个属性使我们能够在理想的$ i \ subset \ mathscr {o} _ {\ mathbbm {c}^n，0} $上提供必要和足够的条件。
The Tjurina ideal of a germ of an holomorphic function $f$ is the ideal of $\mathscr{O}_{\mathbbm{C}^n,0}$ - the ring of those germs at $0\in\mathbbm{C}^n$ - generated by $f$ itself and by its partial derivatives. Here it is denoted by $T(f)$. The ideal $T(f)$ gives the structure of closed subscheme of $(\mathbbm{C}^n,0)$ to the hypersurface singularity defined by $f$, being an object of central interest in Singularity Theory. In this note we introduce \emph{$T$-fullness} and \emph{$T$-dependence}, two easily verifiable properties for arbitrary ideals of germs of holomorphic functions. These two properties allow us to give necessary and sufficient conditions on an ideal $I\subset \mathscr{O}_{\mathbbm{C}^n,0}$, for the equation $I=T(f)$ to admit a solution $f$.
