Timeline for What is deforming this non-complete intersection like?
Current License: CC BY-SA 3.0
9 events
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| Jun 28, 2015 at 22:34 | comment | added | Jason Starr | @DavidTreumann Some non-Cohen-Macaulay ideals deform to Cohen-Macaulay ideals. I am not saying anything about the ideals that can or cannot be obtained by deforming your ideal. I am simply mentioning that your ideal is not Cohen-Macaulay, which is too bad, because otherwise it would be much easier to study your problem. | |
| Jun 28, 2015 at 20:59 | comment | added | David Treumann | Thanks Will and Jason. Jason, can a non-CM ideal be flatly deformed to a CM ideal? Or are you telling me that this variety has no smooth deformations at all! | |
| Jun 28, 2015 at 18:18 | comment | added | Jason Starr | That ideal is, unfortunately, not Cohen-Macaulay (at least if I did my computation correctly). It has an embedded prime $\langle y,u,v\rangle$. That is unfortunate: if it were Cohen-Macaulay, then the Hilbert-Burch-(Schaps) Theorem would describe all flat deformations via variation of a matrix of polynomials (in particular, infinitesimal deformations would always be unobstructed). | |
| Jun 28, 2015 at 3:33 | history | edited | David Treumann | CC BY-SA 3.0 |
wrong equations
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| Jun 28, 2015 at 3:22 | comment | added | Will Sawin | One might try to embed the ideal in the simplest way in $\mathbb P^4$, compute its Hilbert polynomial, and try to understand the appropriate Hilbert scheme. | |
| Jun 28, 2015 at 2:44 | history | edited | Allen Knutson | CC BY-SA 3.0 |
made title more specific to the question
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| S Jun 28, 2015 at 2:44 | history | suggested | Michael Albanese | CC BY-SA 3.0 |
Put math in MathJax.
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| Jun 28, 2015 at 2:26 | review | Suggested edits | |||
| S Jun 28, 2015 at 2:44 | |||||
| Jun 28, 2015 at 1:50 | history | asked | David Treumann | CC BY-SA 3.0 |