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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 : 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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