1. Statement

2. See also

3. References

In mathematics, the Bott residue formula, introduced by {{harvs|txt|last=Bott|year=1967|authorlink=Raoul Bott}}, 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 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

See also

• Atiyah–Bott fixed-point theorem
• Holomorphic Lefschetz fixed-point formula

References

• {{Citation | last1=Bott | first1=Raoul | author1-link=Raoul Bott | title=Vector fields and characteristic numbers | url=http://projecteuclid.org/euclid.mmj/1028999721 | doi=10.1307/mmj/1028999721 | mr=0211416 | year=1967 | journal=The Michigan Mathematical Journal | issn=0026-2285 | volume=14 | pages=231–244}}
• {{Citation | last1=Griffiths | first1=Phillip | author1-link=Phillip Griffiths | last2=Harris | first2=Joseph | author2-link=Joe Harris (mathematician) | title=Principles of algebraic geometry | publisher=John Wiley & Sons | location=New York | series=Wiley Classics Library | isbn=978-0-471-05059-9 | mr=1288523 | year=1994}}

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