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
gollark: I don't think much can practically be done at this point outside of just trying to bodge the climate into sort of working via geoengineering of some kind.
gollark: Don't blame *capitalism* for people being non-long-term.
gollark: You also seem to have said that how stars work is unknown?
gollark: I like unfathomable.
gollark: There was a self replicator built in CGoL some years back. It's hilariously complex and I think involves a universal constructor machine and computer thing.
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
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.