Fano varieties: from derived categories to geometry via stability

Arend Bayer (University of Edinburgh)

05-Mar-2021, 20:00-21:00 (23 months ago)

Abstract: A Fano variety $X$ can be reconstructed from its bounded derived category $D^b(X)$. How to use this fact to extract concrete geometric information from $D^b(X)$? In this talk, I will survey one such approach, via certain subcategories of $D^b(X)$ called Kuznetsov components, and stability conditions. Via moduli spaces of stable objects inside Kuznetsov components, this naturally leads to the reconstruction of many natural moduli spaces classically associated to $X$. In addition to results by a number of authors for Fano threefolds, I will also discuss work in progress (joint with Bertram, Macri, Perry) for cubic fourfolds. Combined with studying Brill-Noether loci, this leads to the construction of special surfaces on an infinite sequence of Hassett-special cubic fourfolds. In some cases, this leads to a natural reinterpretation of recent proofs of rationality of such cubic fourfolds via wall-crossing.

algebraic geometry

Audience: researchers in the topic

( slides | video )

If you have registered once, you are always registered for the seminar, and can join any future talk using the link you receive by email. If you lose the link, feel free to reregister. This might work too: stanford.zoom.us/j/95272114542

More seminar information (including slides and videos, when available): agstanford.com

 Organizer: Ravi Vakil* *contact for this listing

Export talk to