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
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
See also
Atiyah–Bott fixed-point theorem Holomorphic Lefschetz fixed-point formula
References