3 problems

Affine paving conjecture. There exist affine pavings of ${}^0\operatorname{Hilb}^{(m)}(V)$ and $Z^{(m)}(V)$ by the parts $S_T^{\rm new}$ and $S_{\widehat{T}}$, respectively, such t…

Let $G=(G_1,\ldots,G_{n-1}):\mathbb{C}^n\to\mathbb{C}^{n-1}$ be a polynomial mapping with $n\geq 2$ and $K_0(G)=\emptyset$. Assume that there exists a very good projection with res…

Goresky–MacPherson cellular deformation-retraction conjecture. There exists a $\nabla f$-like vector field $V$ on $X$ such that, with