How does one prove that the complete intersection of a quadric and a cubic of $\mathbb P^5$ is unirational?
The question is stated in the title, but I would like to add some motivation. I've been teaching a course on complex tori and abelian varieties this semester and I would like to end it by showing ...
Let $X$ be a projective Fano 3-fold or 4-fold and let $D^b(X)$ be the bounded derived category of coherent sheaves on $X$. For what $X$ is it known a semi orthogonal decomposition into indecomposable ...