Timeline for Infinitely many minimal models
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 9, 2011 at 22:56 | vote | accept | John L. | ||
| Sep 15, 2011 at 14:33 | comment | added | user5117 | Dear ulrich: you're right, people aren't always very careful to say exactly what they mean by "minimal model". (Here by "people" I mean "authors", not the OP.) | |
| Sep 15, 2011 at 14:24 | comment | added | naf | @Artie: By minimal model of $X$ I assumed one means a variety $Y$ that is the end result of running the MMP on $X$. If $X$ is Calabi-Yau then the canonical bundle is nef so the MMP ends at $X$ itself. But having read the question again I agree that this is probably not the definition the OP has in mind. | |
| Sep 15, 2011 at 14:10 | answer | added | user5117 | timeline score: 6 | |
| Sep 15, 2011 at 13:56 | comment | added | user5117 | Also, note that the OP is asking about marked minimal models, which introduces even more non-uniqueness into the picture! | |
| Sep 15, 2011 at 13:55 | comment | added | user5117 | Dear ulrich, I'm not sure I understand your comment. (Terminal) Calabi--Yaus are certainly their own minimal models, but there's no reason they should be unique: if $f:X \dashrightarrow X'$ is a birational map of Calabi--Yaus, then each one is a minimal model of the other, but they need not be isomorphic. | |
| Sep 15, 2011 at 5:57 | comment | added | naf | Calabi-Yau varieties have, by definition, (numerically) trivial canonical bundles so are their own unique minimal models. Perhaps you meant to ask something different? | |
| Sep 15, 2011 at 1:32 | history | asked | John L. | CC BY-SA 3.0 |