Hodge theory

Last modified date: <%+ tp.file.last_modified_date() %>

- Tags: - #MOC - Refs: - REU project: http://math.uchicago.edu/~may/REU2018/REUPapers/Sheagren.pdf#page=1 - More detailed notes: https://scholar.harvard.edu/files/pspark/files/harvardminorthesis.pdf#page=3 - Links: - Hodge decomposition - Hodge symmetry - Hodge weight - Hodge filtration - Hodge diamond - elliptic operator - VHS - Unsorted/Hodge-Tate theory - tangent bundle - Sobolev space - examples of computations of Hodge numbers - period

Hodge theory

attachments/Pasted%20image%2020220503103628.png attachments/Pasted%20image%2020220503103640.png attachments/Pasted%20image%2020220503103754.png

attachments/Pasted%20image%2020220424180556.png

de Rham theorem

attachments/Pasted%20image%2020220424181417.png

Hodge star

attachments/Pasted%20image%2020220424181509.png attachments/Pasted%20image%2020220424181529.png attachments/Pasted%20image%2020220424181843.png

attachments/Pasted%20image%2020220424183028.png attachments/Pasted%20image%2020220424182905.png

Hodge Laplacian

An elliptic operator.

attachments/Pasted%20image%2020220424181605.png attachments/Pasted%20image%2020220424181614.png attachments/Pasted%20image%2020220424181625.png

Hodge decomposition

attachments/Pasted%20image%2020220424181652.png attachments/Pasted%20image%2020220424181659.png attachments/Pasted%20image%2020220424181732.png

Bar duality

attachments/Pasted%20image%2020220424181803.png

Dolbeaut derivative

attachments/Pasted%20image%2020220424181824.png attachments/Pasted%20image%2020220424181855.png attachments/Pasted%20image%2020220424181911.png

See kahler manifold

Hodge theorem and Hodge diamond

attachments/Pasted%20image%2020220424182022.png

Links to this page
#MOC