Timeline for Complex manifold with subvarieties but no submanifolds
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
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| May 9, 2016 at 14:08 | vote | accept | Michael Albanese | ||
| May 9, 2016 at 14:08 | answer | added | Michael Albanese | timeline score: 13 | |
| May 2, 2016 at 17:00 | answer | added | inkspot | timeline score: 32 | |
| May 2, 2016 at 16:19 | comment | added | Jason Starr | My suggestion will not work. Ljudmila Kamenova reminded me that for a generic deformation of $Y$, the subvariety $E$ does not deform. | |
| May 2, 2016 at 16:01 | comment | added | Jason Starr | The following example does not quite work, but perhaps it can be made to work. Let $X$ be a generic Kaehler K3 surface. Let $n\geq 3$ be an integer. Consider the Douady space $Y=\text{Hilb}^n_{X/\mathbb{C}}$ parameterizing closed analytic subspaces of $X$ that are zero-dimensional of length $n$. There is a singular closed analytic hypersurface $E$ in $Y$, namely the locus parameterizing closed subspaces that have at least one point that is nonreduced. Sadly, the deepest stratum of the singular locus of $E$ is a manifold! What if we deform $(Y,E)$ with one multiple point? | |
| May 2, 2016 at 14:46 | history | asked | Michael Albanese | CC BY-SA 3.0 |