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Holomorphic Lefschetz fixed-point formula : ウィキペディア英語版
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
: \sum_\frac = \sum_q(-1)^q\operatorname(f^
*|H^_(M))
where
*The sum is over the fixed points ''p'' of ''f''
*The linear transformation ''A''''p'' is the action induced by ''f'' on the holomorphic tangent space at ''p''

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