Asymptotics of orbifold Bergman kernels: mixed curvature case

We derive some asymptotic expansion formulas of the Bergman kernel of high tensor powers of an Hermitian orbifold line bundle with mixed curvature tensored with an orbifold vector bundle on a compact symplectic orbifold. In particular, when the orbifold has isolated singularities, we get an explicit formula for the asymptotic expansion of the Bergman kernel in the distribution sense. Finally, by applying our results to the complex case, we get a Riemann–Roch–Kawasaki type formula.