We generalize the classical Grothendieck's residue Res ψ/s to virtual cases, which
means the zero loci Z of s has positive dimension. The analogously defined
virtual residue admits an integration form by using complex Berezin integral.
It becomes localized Euler number via Mathai-Quillen formalism. For the case ψ vanishes along the Z upto enough order, we can represent the residue as a pairing between cohomology classes of obstruction sheaves over Z.
Permanent URL for this record: https://lbezone.hkust.edu.hk/bib/b1302286