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 a chart of Nicolas Addington, whose comments shaped the website.

As with my other websites it is a static site built with Hugo. Feature requests, corrections and contributions are very welcome, on GitHub or by email.

LLMs were used to build this, which made the whole process much faster.