Holomorphic Lefschetz fixed-point formula
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
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See also
References
- Griffiths, Phillip; Harris, Joseph (1994), Principles of algebraic geometry, Wiley Classics Library, New York: John Wiley & Sons, ISBN 978-0-471-05059-9, MR 1288523
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