4 problems

Minimal-rank conjecture. Every uniform vector bundle $\mathcal{F}$ on $\mathbb{P}^n$ of rank $<2n$ is homogeneous.

Let $k$ be a positive integer, and let ${\mathcal E}$ be a $k$-type uniform vector bundle on ${\mathbb P}^n$. Consider integers $\alpha_j$ and $\beta$ satisfying $\alpha_j\geq 0$ f…

Let ${\mathcal E}$ be a $k$-type uniform Steiner bundle, where $k$ is the lowest degree of its splitting type. The authors propose a construction technique for such bundles. Constr…

Let $k$ be an algebraically closed field of characteristic zero, and let $\boldsymbol{P}^n$ denote projective $n$-space. A vector bundle on $\boldsymbol{P}^n$ is uniform if its res…