3 problems

Let $\Sigma$ be an $n$-dimensional complete nonsingular fan, let $G(\Sigma)$ be the set of generators of its rays, and let $\ell$ be the Picard number of $\Sigma$. A primitive coll…

Let $\Sigma_1$ and $\Sigma_2$ be smooth fans with the same support. A smooth star subdivision is the subdivision of a fan obtained by inserting the ray through the sum of the primi…

Let $N$ be a lattice and let $\Delta$ be a complete fan on $\mathbb{R}^3$ such that every maximal cone of $\Delta$ is nonsimplicial. Let $B$ be an open neighborhood of $\Delta$ in…