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Nov 6, 2012 at 22:00 comment added Dmitri Panov I see now my mistake (that led me to the question). I was assuming (without any reason) that Satake compactification of $M_g$ is a smooth space. And since Deligne-Mumford is birational to Stake compactification I was thinking that boundary divisors in $\bar M_g$ should be ruled since they have larger dimension than in Satke. This sounded strange to me. But now I see that Satake is singular and so not surprisingly its blow up does not need to contain additional rational curves. Thank you for the answer again.
Nov 6, 2012 at 21:54 vote accept Dmitri Panov
Nov 6, 2012 at 21:30 vote accept Dmitri Panov
Nov 6, 2012 at 21:35
Nov 6, 2012 at 15:16 history answered anon CC BY-SA 3.0