# Fortnightly links (88)

Bumsig Kim, Alexander Polishchuk: Atiyah class and Chern character for global matrix factorizations discusses how one can generalise the Atiyah class calculus which gives a very clean approach for the Hochschild–Kostant–Rosenberg decomposition to the case of (global) matrix factorisations. There is an ever-growing set of analogies between Lie algebras and algebraic geometry, and this forms a really interesting new chapter in it, see also appendix B of Damien Calaque's habilitation thesis.

Eric M. Rains: The birational geometry of noncommutative surfaces is a book-length preprint on noncommutative surfaces that I will not even attempt to do any justice to in a single paragraph. Let me just point out that for example an alternative (but equivalent) approach to noncommutative $\mathbb{P}^1$-bundles is provided. Is anyone up for a reading seminar on this preprint, and/or the earlier The noncommutative geometry of elliptic difference equations by the same author?

I will probably write something about remark 3 in this preprint later this week. I've been intending to write a blogpost about this observation for a while now, and I guess I should really write it now.

Elliptic curves is a fun and well-written browser tool to play around with elliptic curves and their equations. It's very instructive, say for students, to be able to do this from your browser.