Timeline for Constructing affine hypersurfaces with one singularity
Current License: CC BY-SA 2.5
8 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Sep 30, 2010 at 23:06 | vote | accept | James Davidoff | ||
| Sep 30, 2010 at 22:30 | comment | added | James Davidoff | @mdeland: I understand that they are equivalent. I don't understand how this answers my question; you've just rephrased it to "what are conditions on $S$ and/or $H$ such that the weighted projective space is smooth". Having coprime weights that divide the degree is not enough: I can assign degree 2 to $x$ and 1 to $y$ in example 1, and $2|6$, but the singular locus of $x^3$ is not the origin. | |
| Sep 30, 2010 at 22:16 | answer | added | Remke Kloosterman | timeline score: 2 | |
| Sep 30, 2010 at 22:15 | comment | added | mdeland | Yes, you did make it clear - I'm just telling you that the answer to your question is the same as the answer to whether or not the weighted projective hypersurface is smooth. | |
| Sep 30, 2010 at 22:11 | comment | added | James Davidoff | @mdeland; I want to know when the affine hypersurface has such a singularity. I hope I made that clear this time in my question. | |
| Sep 30, 2010 at 22:04 | comment | added | mdeland | This was implicit in the comments to your other question. The associated weighted hypersurface is smooth if and only if the affine hypersurface you're interested in has an isolated singularity at the origin. | |
| Sep 30, 2010 at 20:58 | history | asked | James Davidoff | CC BY-SA 2.5 |