Timeline for Blow-up along a subscheme and along its associated reduced closed subscheme

7 events

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Mar 8, 2012 at 8:05	history	edited	J.C. Ottem	CC BY-SA 3.0	deleted 177 characters in body
Mar 8, 2012 at 4:39	comment	added	Karl Schwede		I believe there is no map from one to the other. In the example J.C. Ottem gives, the blow up of $(x^2,y)$ can be obtained as follows. Blow up $(x,y)$, then blow up another point on that first blowup (the origin on one of the usual charts), and then contract the first exceptional curve. There's no map between $Bl_{(x^2,y)}X$ and $Bl_(x,y) X$, at least no map over $X$.$$\text{ }$$ Just because you have an inclusion of Rees algebras, does not mean that there is an everywhere defined map of the blow-ups. In the given example, one of the points of the overring contracts to an irrelevant ideal.
Mar 7, 2012 at 21:34	history	edited	J.C. Ottem	CC BY-SA 3.0	added 29 characters in body
Mar 7, 2012 at 21:25	comment	added	gio		Thanks for the example. But at least, there is a natural map from one to another?
Mar 7, 2012 at 20:28	history	edited	J.C. Ottem	CC BY-SA 3.0	deleted 606 characters in body
Mar 7, 2012 at 20:15	history	edited	J.C. Ottem	CC BY-SA 3.0	added 165 characters in body
Mar 7, 2012 at 19:48	history	answered	J.C. Ottem	CC BY-SA 3.0