Joints formed by lines and a $k$-plane, and a discrete estimate of Kakeya type

Anthony Carbery, Marina Iliopoulou

Let $\mathcal{L}$ be a family of lines and let $\mathcal{P}$ be a family of $k$-planes in ${\mathbb{F}}^n$ where $\mathbb{F}$ is a field. In our first result we show that the number…