- Alexander Perry, Noncommutative homological projective duality is a preprint which is not (yet) on the arXiv, discussing homological projective duality in a very general setting. Therefore it also deals with noncommutative varieties in the sense that they are only supposed to be sufficiently nice (enhancements of) triangulated categories. Therefore it contains a long discussion of the formalism, which in itself is a very interesting read.
- Alexander Perry, Hochschild cohomology and group actions is another preprint on Alex's website which is not yet on the arXiv. It compares Hochschild cohomology of an equivariant triangulated category with the invariant part of Hochschild cohomology of a triangulated category, in order to compute the Hochschild cohomology of some fractionally Calabi–Yau categories. It's a very nice read.
- Daniel Huybrechts, Cubic hypersurfaces are the course notes for a course currently being taught at the University of Bonn. They are in a state of flux, with regular updates. Both the lectures themselves and the notes are really good.