Timeline for resolution of singularities on surfaces
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 20, 2009 at 16:49 | comment | added | Charles Siegel | Ahh, yeah, I think I see where my mistake was. I concede to jvp and Tony. | |
| Dec 20, 2009 at 16:19 | comment | added | Jorge Vitório Pereira | I am not sure that resolving linear systems is more general than resolving singularities. What I think is clear is the converse: if you consider the closure of the graph of the rational map induced by the linear system you obtain a variety ( blow-up of the original variety at the base scheme of the linear system ) and to finish resolving the original linear system it suffices to resolve the singularities of this variety. | |
| Dec 20, 2009 at 13:51 | comment | added | Charles Siegel | I haven't worked it out, but I expect that it is, because resolving singularities of linear systems and resolving singularities of varieties are extremely similar, and I'm pretty sure that resolving linear systems is more general, so if it can go wrong with varieties, it should be able to go wrong in maps, though I don't have a simple example off the top of my head. | |
| Dec 20, 2009 at 13:37 | comment | added | user2529 | you mean this is the case even if the original surface is nonsingular? | |
| Dec 20, 2009 at 13:30 | history | answered | Charles Siegel | CC BY-SA 2.5 |