differential geometry Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multili ...

, Kawasaki's Riemann–Roch formula, introduced by Tetsuro Kawasaki, is the Riemann–Roch formula for orbifolds. It can compute the

Euler characteristic of an orbifold In differential geometry, the Euler characteristic of an orbifold, or orbifold Euler characteristic, is a generalization of the topology, topological Euler characteristic that includes contributions coming from nontrivial automorphisms. In particula ...

. Kawasaki's original proof made a use of the

equivariant index theorem In differential geometry, the equivariant index theorem, of which there are several variants, computes the (graded) trace of an element of a compact Lie group acting in given setting in terms of the integral over the fixed points of the element. I ...

. Today, the formula is known to follow from the Riemann–Roch formula for quotient stacks.

References

*Tetsuro Kawasaki. The Riemann-Roch theorem for complex V-manifolds. Osaka J. Math., 16(1):151–159, 1979 Theorems in differential geometry Theorems in algebraic geometry

References

See also