Fortnightly links (13)

Nicolas Addington, Brendan Hassett, Yuri Tschinkel, Anthony Várilly-Alvarado: Cubic fourfolds fibered in sextic del Pezzo surfaces comes back to something which is turning into a recurring theme on my blog, which is the (non)rationality of the generic cubic fourfold. This paper rather identifies another class of cubic fourfolds which are special, in the sense that they are rational, unlike what is expected for the generic case.

Evelyn Lamb: Higher Homotopy Groups Are Spooky is a nice popularizing article about homotopy groups. I have to admit I never spent enough time thinking about the implications and interpretations of the higher homotopy groups of spheres, but this article aptly explains why some of those results require a bit of mind-bending, and what they mean in low dimensions.

Atsushi Ito, Makoto Miura, Shinnosuke Okawa, Kazushi Ueda: The class of the affine line is a zero divisor in the Grothendieck ring: via G2-Grassmannians is another proof of the fact that in the Grothendieck ring of varieties (also known as "baby motives") the class of the affine line is a zero-divisor. As in the original approach by Borisov, it uses Calabi–Yau threefolds. Observe that there was a proof by Galkin–Shinder of the non-rationality of the generic cubic fourfold depending on the class of the affine line not being a zerodivisor.

José Rodríguez Alvira: The art of fugue is an interesting guide to Bach's Die Kunst der Fuge, by describing the structure in a really pretty online way.