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Feb 7, 2011 at 10:34 comment added Qing Liu The fact that $W_i$ is the blow-up of $(J_iK_i)O_{V_i}$ can also be done with the universal property of blow-ups, see Raynaud-Gruson: <i>Techniques de platification d'un module</i>, Remarque 5.1.2(v). So in fact $Y\to X$ can factor into $Y\to X_i\to X$ where $X_i\to X$ is the blow-up of $X$ along $I_i$.
Feb 7, 2011 at 10:28 history edited Qing Liu CC BY-SA 2.5
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Jan 30, 2011 at 18:40 history answered Karl Schwede CC BY-SA 2.5