Pieter Belmans

Today's arXiv update includes Joe Waldron and Jakub Witaszek's paper, “An irregular smooth Fano fourfold in positive characteristic”.

After seeing John Christian Ottem, Stable irrationality of quartic sixfolds on the arXiv yesterday, I was reminded of my plans a little while ago to make a website like mgnbar.info surveying the state of the art on a precise question.

Here's a question I have had for a while, ever since reading Noncommutative rigidity of the moduli stack of stable pointed curves by Shinnosuke Okawa and Taro Sano.

After returning from holidays earlier this summer, I organized all the stuff on my desk a bit, and I ran into various half-finished computations and notes.

This post is about The hyperkähler period-index conjecture is false, joint with James Hotchkiss.

There is a new website, hyperelliptic.ncag.info, on the classification of hyperelliptic (or generalized hyperelliptic) varieties in complex dimensions 2, 3 and 4.

Whilst it might look like I am hyperproductive these few weeks, with a new blogpost coming up almost every day about something I have done, I am mostly just putting things online that were finished before, in preparation of the summer holidays.

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.

Back in 2015, Johan Commelin and I made le superficie algebriche, an interactive picture of the geography of minimal complex algebraic surfaces, plotted by their Chern numbers $\mathrm{c}_1^2$ and $\mathrm{c}_2$ (see the original post and a 2019 update).

Some quick housekeeping: several of my websites now have a Zenodo DOI, so they are easier to cite.

Back in 2023, together with Ignacio Barros, I made Mgnbar.info, a website about the geometry of $\overline{\mathrm{M}}_{g,n}$, the moduli space of stable $n$-pointed genus $g$ curves.