Timeline for Singularities of Chow varieties
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 11, 2021 at 12:18 | vote | accept | user127776 | ||
| Nov 10, 2021 at 11:29 | answer | added | Jason Starr | timeline score: 2 | |
| Nov 6, 2021 at 21:55 | comment | added | Jason Starr | The modified Question 1 is still false. Consider the Piene-Schlessinger Theorem and the Chow variety of cubic space curves. | |
| Nov 6, 2021 at 21:34 | comment | added | Jason Starr | The modified Question 2 is still false. Consider the blowing up of the projective plane along the base locus of a very general pencil of plane cubics. | |
| Nov 6, 2021 at 19:54 | comment | added | user127776 | @JasonStarr Thanks for pointing out it me, I've updated the problem statement. | |
| Nov 6, 2021 at 19:53 | history | edited | user127776 | CC BY-SA 4.0 |
Fixed few issues that lead to the trivial answer.
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| Nov 6, 2021 at 9:48 | comment | added | Jason Starr | The first question about LCI singularities fails for $X$ equals to $\mathbb{P}^3$, for $r=0$, and for $d\geq 2$. The point is that the action of the symmetric group $\mathfrak{S}_d$ on the $d$-fold self-product $(\mathbb{P}^3)^d$ is not "unimodular", and thus the quotient as a symmetric product is not Gorenstein, much less LCI. The second question fails if $X$ is a smooth cubic surface: the cycle of $d$ times a line is "rigid" hence gives a connected component that is a point. | |
| Nov 5, 2021 at 18:26 | history | edited | user127776 | CC BY-SA 4.0 |
added 29 characters in body
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| Nov 5, 2021 at 18:20 | history | asked | user127776 | CC BY-SA 4.0 |