This morning I discovered a super awesome visualisation of Calabi–Yau 3-folds. The very same plot of Hodge numbers of Calabi–Yau 3-folds indicated 25 years ago that something like mirror symmetry could be true, and this tool is a spectacular visualisation of what is already known about mirror pairs for Calabi–Yau 3-folds. Make sure you read the documentation properly, and check out the “Open as static max zoom view” button, which gives you a plot of the whole view!

Have you ever encountered the username and password dialog box for MathSciNet whilst accessing it from your home connection? Of course, you could VPN to your institution to gain access, but it is now possible to sidestep this! I was told about this new functionality by Edward Dunne at the AMS Summer Institute in Algebraic Geometry, that allows you to use client-side storage to authenticate you for 90 days (it can be renewed after that), even if you are not using your institution’s connection! The relevant pages are:

An important result in algebraic geometry is the Kodaira–Enriques classification. It is a description of the geography of compact complex surfaces, later extended to surfaces in characteristic $p$. The Wikipedia page contains a wealth of information (seriously, it is one of the best mathematics pages in my opinion), and provides a pretty picture that describes the classification in an easy to remember way.

Together with Johan Commelin I made an interactive version of this picture, where you can get more information about the objects that are involved: more numerical invariants, a short description and references to the literature. You can find it at http://superficie.info. Johan has written a really detailed explanation on his weblog, you should check it out!

It is far from complete, in the sense that we certainly haven’t added every class of surfaces in the literature, and the existing descriptions can be improved. Neither of us is an expert in the birational classification of surfaces, but if you are and you want to contribute please get in touch with us! Also, if you want to contribute to the coding there is the GitHub project.

tl;dr: Go to superficie.info.

Disclaimer: I’m having issues with loading the page on my own computer, but Johan isn’t experiencing any problems. Please tell me if you experience any problems with loading. You should see a grid of dots with some lines on the left, with text and mathematics on the right.

Because of the heat wave currently keeping Belgium in its grip (preventing me from doing research…) I decided to finally make the last fixes for a new feature for the Stacks project that has been in the make now for a while: detailed tag edits.

Git has a feature called git blame, that tells you when a certain line in a file was last edited and by whom. Starting from this idea Johan has built stacks-history that collects all this information throughout the lifetime of the Stacks project for all tags. If you add a little processing code to get this in the database in a meaningful format and some new website code, and you can check exactly when a tag has been changed!

If you want to see it in action, point your browsers to the history page for the tensor-Hom adjunction.

It’s not perfect (it might misinterpret some changes etc.) so if you spot mistakes, please do tell. And if you have suggestions to make this feature (or the Stacks project in general) better, please do tell!

The late Alexander (Sasha) Rosenberg, has a webpage collecting (some of) his work. Of course, most of his works were available through the preprint server of the Max–Planck Institute, but now things are easy accessible. It only went online a few days or weeks ago I think, and I guess it is maintained by his son Leo. There is also a book containing selected papers, which seems to be the print version of the website I linked.

Enjoy!

A little over two years ago I started my Atlas of $\mathop{\mathrm{Spec}}\mathbb{Z}[x]$. Today I added another map, from a (forever draft?) book of David Mumford and Tadao Oda.

I urge you to check out the website of David Mumford, who, despite having switched from algebraic geometry to vision in the 80s maintains an excellent overview of all his work in geometry. In particular, he recently posted this draft version of a book which is over 40 years old, which contains a TeX’ified version of his map of the affine line over the integers on page 120.

Yes, I am still alive. Today I would like to announce a new series of lectures in our graduate student seminar. We are going to talk about Hodge-to-de Rham degeneration, and the proof of Deligne–Illusie of this. Feel free to join in if you are interested, and somewhere in the neighbourhood of Antwerp.