Timeline for Is complete intersection a open or closed property in Hilbert schemes
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| when toggle format | what | by | license | comment | |
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| Jun 21, 2017 at 18:50 | comment | added | David E Speyer | Easier, I think. Consider the Hilbert scheme of $4$ points in $\mathbb{P}^2$. Four general points are the complete intersection of two conics, but if three of the points become colinear, they are not a complete intersection. If all four become colinear, they are a complete intersection but of a different sort: line intersect degree four. | |
| Jun 21, 2017 at 13:16 | review | Close votes | |||
| Jun 21, 2017 at 14:13 | |||||
| Jun 21, 2017 at 12:59 | comment | added | abx | No to both questions. Take for $X$ a complete intersection of 3 quadrics in $\mathbb{P}^4$. A general element of $H$ is of the same type (it is a smooth curve of genus 5 canonically embedded). But $H$ contains closed points corresponding to trigonal curves of genus 5, and these are not complete intersections. | |
| Jun 21, 2017 at 12:47 | history | asked | Ron | CC BY-SA 3.0 |