Let $(X,x)$ be an affine variety with a normal isolated singularity and $Y$ be a smoothing of $X$ (for this we mean $Y$ can be realized as a smooth fibre of a deformation of $X$).

Question. Can it happen that the topology of $Y$ is nontrivial, i.e. $\pi_i(Y)\neq \{1\}$ for some $i\geq 1$? Here the topology is induced from the analytic structure instead of the Zariski topology.

Let $(X,x)$ be an affine variety with a normal isolated singularity and $Y$ be a smoothing of $X$ (for this we mean $Y$ can be realized as a smooth fibre of a deformation of $X$).

Question. Can we say that the topology of $Y$ is nontrivial, i.e. $\pi_i(Y)\neq \{1\}$ for some $i\geq 1$? Here the topology is induced from the analytic structure instead of the Zariski topology.

Let $(X,x)$ be an affine variety with normal isolated singularity and $Y$ be a smoothing of $X$ (for this we mean $Y$ can be realized as a smooth fibre of a deformation of $X$). Can we say the topology of $Y$ is nontrivial, i.e. $\pi_i(Y)\neq 0$ for some $i\geq 0$ (Here the topology is induced from the analytic structure instead of the Zariski topology)?

Let $(X,x)$ be an affine variety with a normal isolated singularity and $Y$ be a smoothing of $X$ (for this we mean $Y$ can be realized as a smooth fibre of a deformation of $X$).

Question. Can it happen that the topology of $Y$ is nontrivial, i.e. $\pi_i(Y)\neq \{1\}$ for some $i\geq 1$? Here the topology is induced from the analytic structure instead of the Zariski topology.