Kawasaki’s formula is a tool to compute holomorphic Euler characteristics of vector bundles on a
compact orbifold
.
Let
be
an orbispace with perfect obstruction theory which admits an embedding in a smooth
orbifold. One can then construct the virtual structure sheaf and the virtual fundamental
class of
.
In this paper we prove that Kawasaki’s formula “behaves well” with working “virtually”
on
in
the following sense: if we replace the structure sheaves, tangent and normal
bundles in the formula by their virtual counterparts then Kawasaki’s
formula stays true. Our motivation comes from studying the quantum
-theory of a
complex manifold
(Givental and Tonita, 2014), with the formula applied to Kontsevich moduli spaces of
genus- stable
maps to
.
