All Questions

Let $f\in \mathbb{C}[x_1, \dots,x_n]$ be a homogeneous polynomial of degree $p$ and let $F \in \mathbb{C}[x_1, \dots,x_n,t]$ be a polynomial such that $F(x_1, \dots, x_n,0)=f$, for every $t_0$ we have ...

Consider $f \in \mathbb{C}\{x_1,\dots,x_n\}$ such that $(V(f),0)$ has an isolated singularity. Let $F \in \mathbb{C}\{x_1,\dots,x_n,t\}$ be a deformation of $f$ such that there exists some integer $m$...

Let $V$ be a variety over $\mathbb{C}$ and suppose $O$ is a singular point of $V$. Are there conditions on $(V,O)$ such that a versal deformation $W$ of $(V,O)$ has only quasi-ordinary singularities. ...

Let $R$ be a local singularity (for example $R=\mathbb{C}[[x_1, \ldots , x_n]]/I$) ring over $\mathbb{C}$. Let $\mathbb{L}_{R}$ be a cotangent complex of $R$, then one can define tangent (Andre-...