All Questions

Let $X$ be a singular projective variety. Denote by $Z$ the singular locus of $X$. Consider the resolution of singularities $$\pi: \widetilde{X} \to X$$ Denote by $E$ the exceptional divisor. We know ...

Let $X \subset \mathbb{C}^n$ be a simply connected complex variety with a unique isolated singularity at $x\in X$. Let $\tilde{X}$ be the strict transform of $X$ under the blow-up $\mathrm{Bl}_x(\...

Is it possible to have a 2 dimensional foliation of $\mathbb{R}^{3}-\{0\}$ such that each leaf is homeomorphic to the torus? what algebraic topological obstruction exist? Another question: is there ...