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Bott residue formula
Theorem about complex manifolds
Theorem about complex manifolds
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 A**p 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
References
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