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Mar 4 at 19:14 comment added Leo Herr I want to understand the intersection complex of the boundary of M0n. In some of these constructions, e.g. M0n --> Ln, there are more components of the boundary of M0n than Ln. The intersection complex can't be obtained by blowing up components alone, but hopefully first by doing so and then by adding some divisors which are normal-crossings with the preexisting boundary divisors of Ln.
Mar 4 at 14:43 history edited Dan Petersen CC BY-SA 4.0
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Mar 3 at 21:28 comment added Dan Petersen Also a question: what do you mean by "adding divisors" in your question?
Mar 3 at 21:25 history answered Dan Petersen CC BY-SA 4.0