This post is about The hyperkähler period-index conjecture is false , joint with James Hotchkiss. If I were still posting fortnightly links, Alexander Perry: The period-index conjecture is false would have prominently featured, because it disproves (as the title suggests) the period-index conjecture, which is famously a theorem due to de Jong in dimension 2, with a beautiful proof. But Alex found…
There is a new website, hyperelliptic.ncag.info , on the classification of hyperelliptic (or generalized hyperelliptic ) varieties in complex dimensions 2, 3 and 4. For now it lives as a subdomain of ncag.info. A hyperelliptic variety is a quotient $X = T/G$ of a complex torus $T$ by a finite group $G$ acting freely and without translations. In dimension 1 these are the elliptic curves, in…
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. This post is about Fano 4-fold quiver moduli from subspace quivers , a new paper joint with Markus Reineke. Let's discuss the origin story of this paper in…
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…
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 ). It has just had its biggest update since. A table. Next to the plane of Chern numbers there is now a table : every class of surface in the…
Some quick housekeeping: several of my websites now have a Zenodo DOI, so they are easier to cite. This currently covers fanography.info , grassmannian.info , hyperkaehler.info and mgnbar.info , with more to follow. Each site's 'how to cite' section now lists the DOI, and I use the version-independent one, so it always resolves to the latest release. If you use any of these in your work, please do…
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. For a long time it showed a single invariant, the Kodaira dimension. It now has two more layers, which you can pick from the selector above the table, and the Kodaira dimension layer itself has gained some extra…
I'm happy to announce a new paper, Brauer groups of resolved quiver moduli via gerbes , joint with Gianni Petrella and Sebastian Torres . In this paper we give a new and very different proof of an old result due to Le Bruyn and Schofield (two mathematicians I admire greatly!), by translating a proof (due to Biswas–Hogadi–Holla) in the context of moduli of vector bundles on curves to…
I want to congratulate Gianni Petrella , for his PhD defense today at the University of Luxembourg, and the wonderful thesis Windows, walls and invariants of quiver moduli that he has written. The thesis will be available online at some point, but you can also check out the papers it builds on: Rigidity and Schofield's partial tilting conjecture for quiver moduli , a joint paper with Ana-Maria…
Almost eight years ago I launched Fanography . It has just received its biggest technical overhaul since then: fanography.info is now a static website, generated with Hugo and served from GitHub Pages. From Flask to Hugo Before, Fanography was a Flask application: a little Python server that assembled each page on the fly from the underlying classification data. That worked well, but it meant…