0
votes
0answers
231 views

Local System and Gauss-Manin connection

Fix a complex manifold $X$. Then if we have a line bundle $L=\mathcal{O}(D)$ together with Gauss-Manin connection $\nabla: L \rightarrow L \otimes \Omega^{1}_X$, we get the locally constant sheaf $F$ ...
3
votes
3answers
315 views

When can Hodge filtrations (decompositions?) be described explicitly in terms of periods?

It seems that there is no chance to explain the Hodge theory (to students) in an hour or so. Yet do there exist any cases when the Hodge filtration (or the Hodge decomposition) of the cohomology of a ...
3
votes
1answer
251 views

de Rham cohomology class of diagonal

I post again a question I asked in the post by Descartes: Since this is the topic on diagonal, I like to ask a question: Let $X$ be a compact Kahler manifold of complex dimension $n$, and let $\Delta ...