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SUMMARY:Verlinde formulas on surfaces - Lothar Goettsche (Abdus Salam Inte
 rnational Centre for Theoretical Physics)
DTSTART:20240620T090000Z
DTEND:20240620T100000Z
UID:TALK217684@talks.cam.ac.uk
DESCRIPTION:Let $S$ be a smooth projective surface with p_g>0 and H^1(S\,\
 \Z)=0.&nbsp\;&nbsp\;We consider the moduli spaces $M=M_S^H(r\,c_1\,c_2)$ o
 f $H$-semistable sheaves on $S$ of rank $r$ and&nbsp\;with Chern classes $
 c_1\,c_2$. Associated a suitable class $v$ the Grothendieck group of vecto
 r bundles&nbsp\;on $S$ there is a deteminant line bundle $\\lambda(v)\\in 
 Pic(M)$\, and also a tautological sheaf $\\tau(v)$ on M.In this talk we de
 rive a conjectural generating function for the virtual Verlinde numbers\, 
 i.e. the virtual holomorphic&nbsp\;Euler characteristics of all determinan
 t bundles $\\lambda(v)$ on M\, and for Segre invariants associated to $\\t
 au(v)$.&nbsp\;The argument is based on conjectural blowup formulas and a v
 irtual version of Le Potier's strange duality.&nbsp\;Time permitting we al
 so sketch a common refinement of these two conjectures\, and their proof f
 or Hilbert schemes of points.
LOCATION:Seminar Room 1\, Newton Institute
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