Timeline for Is the Chow scheme of 1-cycles the space of Cohen-Macaulay curves?
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11 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
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| S Aug 22, 2016 at 22:02 | history | bounty ended | CommunityBot | ||
| S Aug 22, 2016 at 22:02 | history | notice removed | CommunityBot | ||
| Aug 15, 2016 at 14:51 | comment | added | Brenin | @JasonStarr So at least as points Chow is the union of these finitely many Hilbert schemes of CM curves. Do you think they are in fact its connected components? It looks like the arithmetic genus is the only discrete invariant left. But do we even have an immersion $I_{1-g}^{CM}(Y,\beta)\to CH_1(Y,\beta)$? | |
| S Aug 14, 2016 at 20:25 | history | bounty started | Brenin | ||
| S Aug 14, 2016 at 20:25 | history | notice added | Brenin | Authoritative reference needed | |
| Aug 12, 2016 at 17:55 | history | edited | Brenin | CC BY-SA 3.0 |
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| Aug 12, 2016 at 17:39 | comment | added | Jason Starr | I was confused about the term irreducible class. If by irreducible class you mean a class that can be decomposed (nontrivially) as a sum of other effective curve classes, then you are correct that you cannot have nonreduced structure. However, a decomposable class can be represented by an irreducible curve. | |
| Aug 12, 2016 at 17:09 | comment | added | Brenin | I know there can be fat components on a CM curve, but can this happen for irreducible homology classes? My point was that if $\beta$ is irreducible, all curves in that class are reduced, and Hilb does not contain points corresponding to nonreduced curves. Is it wrong? | |
| Aug 12, 2016 at 16:23 | comment | added | Jason Starr | A Cohen-Macaulay curve can still be nonreduced, i.e., some primary ideals of minimal primes need not be prime. There are typically moduli of that nonreduced structure. The Hilbert scheme sees those moduli, but the Chow scheme does not. | |
| Aug 12, 2016 at 13:59 | history | asked | Brenin | CC BY-SA 3.0 |