Fano varieties: from derived categories to geometry via stability
Arend Bayer (University of Edinburgh)
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 )
Stanford algebraic geometry seminar
Series comments: This seminar requires both advance registration, and a password. Register at stanford.zoom.us/meeting/register/tJEvcOuprz8vHtbL2_TTgZzr-_UhGvnr1EGv Password: 362880
If you have registered once, you are always registered, and can just join the talk. Link for talk once registered: in your email, or else probably: stanford.zoom.us/j/95272114542
More seminar information (including slides and videos, when available): agstanford.com
Organizer: | Ravi Vakil* |
*contact for this listing |