Bott residue formula

In mathematics, the Bott residue formula, introduced by, describes a sum over the fixed points of a holomorphic vector field of a compact complex manifold.

Statement
If v is a holomorphic vector field on a compact complex manifold M, then
 * $$ \sum_{v(p)=0}\frac{P(A_p)}{\det A_p} = \int_M P(i\Theta/2\pi)$$

where
 * The sum is over the fixed points p of the vector field v
 * The linear transformation Ap is the action induced by v on the holomorphic tangent space at p
 * P is an invariant polynomial function of matrices of degree dim(M)
 * Θ is a curvature matrix of the holomorphic tangent bundle