- Statement
- See also
- References
In mathematics, the Holomorphic Lefschetz formula is an analogue for complex manifolds of the Lefschetz fixed-point formula that relates a sum over the fixed points of a holomorphic vector field of a compact complex manifold to a sum over its Dolbeault cohomology groups.
Statement
If f is an automorphism of a compact complex manifold M with isolated fixed points, then
where
- The sum is over the fixed points p of f
- The linear transformation Ap is the action induced by f on the holomorphic tangent space at p
See also
- Bott residue formula
References
- {{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}}
2 : Complex manifolds|Theorems in algebraic geometry
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