Cubic 4-folds: special cubic fourfolds and their K3 surfaces

Since early 2023 there has been a website at cubics.fanography.info on the relationship between cubic fourfolds and K3 surfaces, but I never announced it I think: a first draft version was written in just 2 days and I didn’t know what to do next. I’m not sure it is in any state or form “finished”, but given that I’m on a website spree lately, I might as well get this one out too. So this is that announcement, three years late. Hassett divisors A smooth cubic fourfold $X\subseteq\mathbb{P}^5$ is special if it contains a surface not homologous to a complete intersection; these form the Hassett divisors $\mathcal{C}_d$ in the moduli space of cubic fourfolds. The website is a table with one row for every discriminant $d$, collecting some things that are known about $\mathcal{C}_d$: the various notions of an associated (twisted) K3 surface, rationality, the Kodaira dimension, Fourier–Mukai partners, and which surfaces the generic member contains, with clickable references. It goes back to…