# Fortnightly links (164)

We're back with the regular scheduling after having taken the Christmas break off.

Steve Trettel: Barth sextic in $\mathrm{S}^3$ is a beautiful visualisation of the Barth sextic, not in an affine patch but rather the double cover ramified in the Barth sextic restricted to $\mathrm{S}^3$ which does manage to capture all of geometry in a single chart. These pictures are

**stunning**! I wish I could reproduce these and play around with some other surfaces, this is really super cool.More tweets by Steve Trettel with similar pictures: tweet 1, tweet 2

James Hotchkiss: Hodge theory of twisted derived categories and the period-index problem and Aise Johan de Jong, Alexander Perry: The period-index problem and Hodge theory are two preprints discussing the period-index problem using Hodge theory, the former on the categorical side, the latter in a more classical setting. They both look really interesting at first sight, and I'll read them a bit later this week or the next.

Olivier Debarre: On rationality problems are lecture notes on rationality questions in algebraic geometry. For a recent update on the state-of-the-art of this question, this is a very nice reference and introduction!