This update is concerned with Moduli spaces of semiorthogonal decompositions in families, written together with Shinnosuke Okawa, and Andrea Ricolfi. I already alluded to it in the previous post: this paper has seen a significant update.

What's new?

Following a very useful referee report, we have:

  • streamlined the entire paper;
  • referred to the literature for étale descent of semiorthogonal decompositions, thereby getting rid of a characteristic-zero assumption;
  • included a second proof of the functor being limit-preserving, following a suggestion by the referee;
  • included the referee's proof for uniqueness of deformations (with the original proof moved to a separated paper);
  • everything now works in a general smooth and proper setting, so the standing assumptions are always the same;
  • we have expanded the discussion on our conjecture regarding the subspace of non-trivial semiorthogonal decompositions.

I believe the paper is much improved now, so if you didn't like the previous version, you can give this one a shot!