Again 2 days late, and I haven't written about the new Stacks project website. Stay tuned.

  • The following is an unusual fortnightly link, as I usually don't link to persons. But this one is special. Meet Xena. Her father describes her as follows.

    Xena is a student at Imperial College London in the mathematics department. Xena is a bit of a strange one. Firstly, she doesn’t really speak much English. Secondly, in some real sense she knows far less mathematics than the typical undergraduate in their first year at Imperial College (I am pretty sure that she currently has no idea that the derivative of $\sin(x)$ is $\cos(x)$ for example, which is a standard result that we would expect all of our beginning undergraduates to know).

    As is also advertised on Xena's blog, she very recently learned the definition of a scheme. They are slowly working through some of the basic tags in the Stacks project. Any bets on how long it will take her to learn about the Deligne–Mumford theorem? For your information, this result depends on 6461 tags!

  • Nicolas Addington, Andrew Wray: Twisted Fourier–Mukai partners of Enriques surfaces is a fun paper, showing that any derived equivalence $\mathbf{D}^{\mathrm{b}}(X,\alpha)\simeq\mathbf{D}^{\mathrm{b}}(Y,\beta)$ such that $X$ is a (complex) Enriques surface and $\alpha\in\operatorname{Br}(X)\cong\mathbb{Z}/2\mathbb{Z}$ is a Brauer class implies that $X\cong Y$ mapping $\alpha$ to $\beta$. Any regular reader of my fortnightly links should realise that I like these kinds of results!

    The fact that $\operatorname{Br}(X)\cong\mathbb{Z}/2\mathbb{Z}$ is proven by Beauville, using the $2:1$-cover by a K3 surface (or maybe this fact should be considered as standard), in a paper where he also studies the image under pullback along this cover of the non-zero element.