BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Counting sheaves on Calabi-Yau 4-folds - Jeongseok Oh\, Imperial C
 ollege London
DTSTART:20221019T131500Z
DTEND:20221019T141500Z
UID:TALK178934@talks.cam.ac.uk
CONTACT:Dhruv Ranganathan
DESCRIPTION:Borisov-Joyce constructed a real virtual cycle on compact modu
 li spaces of stable sheaves on Calabi-Yau 4-folds\, using derived differen
 tial geometry. We constructed an algebraic virtual cycle. A key step is a 
 localisation of Edidin-Graham's square root Euler class for SO(2n\,C) bund
 les to the zero locus of an isotropic section\, or to the supprot of an is
 otropic cone.\nWe also develop a theory of complex Kuranishi structures on
  projective schemes which are sufficiently rigid to be equivalent to weak 
 perfect obstruction theories\, but sufficiently flexible to admit global c
 omplex Kuranishi charts. We apply the theory to the moduli spaces to prove
  the two virual cycles coincide in homology after inverting 2 in the coeff
 icients. In particular\, when Borisov-Joyce's real virtual dimension is od
 d\, their virtual cycle is torsion.\nThis is a joint work with Richard Tho
 mas.
LOCATION:CMS MR13
END:VEVENT
END:VCALENDAR