Solitons: Differential equations, symmetries, and infinite-dimensional algebras
《Solitons: Differential equations, symmetries, and infinite-dimensional algebras》 · 第 169 页 · Exercise 6.10
Let $X$ be a scheme locally of finite type over a field $k$, let $x\in X(k)$, and let $\mathfrak m=\mathfrak m_x$ be the maximal ideal at $x$. Then $A:=\bigoplus_{d\ge0}\mathfrak m^d/\mathfrak m^{d+1}$ is a $k$-algebra. The affine scheme $\operatorname{TC}_x(X):=\operatorname{Spec}A$ is called the tangent cone of $X$ at $x$.