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2 votes
0 answers
62 views

Base change for finding fibers of the pushforward of a line bundle along a proper non-flat morphism

Let $f: X \to Y$ be a proper morphism whose fibers have different dimensions, in particular $f$ is not flat. Let $L$ be a line bundle on $X$. What conditions would be sufficient to be able to conclude ...
4 votes
2 answers
1k views

Different definition of sheaf cohomology

It could be related to my previous question here. Let $\mathcal F$ be a sheaf on a topological space $X$. Hartshorne in his book on Algebraic geometry defines the sheaf cohomology by $$ H^i(X, \...