4 problems

Let $Y$ be a complex analytic manifold and let $f:Y\to\Delta$ be a projective morphism, where $\Delta$ is a disc. A morphism is a homotopy fiber bundle if it has the homotopy-local…

Whitney's fibering conjecture. Every analytic subvariety $V\subset U$ has a stratification such that each point $p_0\in V$ has a neighborhood $U_0$ with a semi-analytic fibration.

Let $(V(f),\0) \subseteq ({\mathbb C}^3,\0)$ be a reduced hypersurface with $\dim_\0 \Sigma f=1$, and suppose that the normalization of $V(f)$ is a bijection. Lê's conjecture. Then…

Excellence conjecture. If $\mu_I$ is constant, then the unfolding is excellent.