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SUMMARY:Arend Bayer (University of Edinburgh)
DTSTART:20210305T200000Z
DTEND:20210305T210000Z
DTSTAMP:20260407T214324Z
UID:agstanford/41
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/agstanford/4
 1/">Fano varieties: from derived categories to geometry via stability</a>\
 nby Arend Bayer (University of Edinburgh) as part of Stanford algebraic ge
 ometry seminar\n\n\nAbstract\nA Fano variety $X$ can be reconstructed from
  its bounded derived category $D^b(X)$. How to use this fact to extract\nc
 oncrete geometric information from $D^b(X)$? \nIn this talk\, I will surve
 y one such approach\, via certain subcategories of $D^b(X)$ called Kuznets
 ov components\, and stability conditions. Via moduli spaces of stable obje
 cts inside Kuznetsov components\, this naturally leads to the reconstructi
 on of many natural moduli spaces classically associated to $X$. \nIn addit
 ion to results by a number of authors for Fano threefolds\, I will also di
 scuss work in progress (joint with Bertram\, Macri\, Perry) for cubic four
 folds. Combined with studying Brill-Noether loci\, this leads to the const
 ruction of special surfaces on an infinite sequence of Hassett-special cub
 ic fourfolds. In some cases\, this leads to a natural reinterpretation of 
 recent proofs of rationality of such cubic fourfolds via wall-crossing.\n
LOCATION:https://researchseminars.org/talk/agstanford/41/
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