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Jun 30, 2018 at 22:59 vote accept user2520938
Jun 30, 2018 at 15:59 answer added Donu Arapura timeline score: 5
Jun 30, 2018 at 10:57 comment added Jason Starr Can you please clarify your notation? By my computation, your short exact sequence is correct only if you define the closed subsets $D_j$ to be the connected components of $D$ rather than the irreducible components. Anyway, the connecting map $H^0(D,\mathcal{O}_D) \to H^1(X,\Omega^1_X)$ is the map that sends the generator of each connected component $D_i$ to its cycle class in de Rham cohomology. So the kernel of the connecting map is generated by homological equivalences among the components $D_j$ of $D$.
Jun 30, 2018 at 8:32 history asked user2520938 CC BY-SA 4.0