Timeline for Is being of general type stable under generization
Current License: CC BY-SA 4.0
15 events
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| Feb 26, 2020 at 8:24 | history | edited | Ariyan Javanpeykar | CC BY-SA 4.0 |
fixed some typos
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| Jan 29, 2019 at 12:30 | comment | added | Frank | It would be interesting to know if there's an unconditional proof of the statement about Kodaira dimension. @EvgenyShinder do you have an idea how one can use your motivic specialisation maps to pass information about plurigenera instead of (stable) birational type? | |
| S Jan 25, 2019 at 7:18 | history | bounty ended | Ariyan Javanpeykar | ||
| S Jan 25, 2019 at 7:18 | history | notice removed | Ariyan Javanpeykar | ||
| Jan 25, 2019 at 7:17 | vote | accept | Ariyan Javanpeykar | ||
| Jan 24, 2019 at 13:08 | answer | added | Frank | timeline score: 11 | |
| Jan 24, 2019 at 10:06 | comment | added | Jason Starr | @EvgenyShinder. "... if $X$ has Kodaira dimension $m$, then every component of a degeneration of $X$ has Kodaira dimension bounded by $m$? Is this false?" I am just making the same observation as in my previous comment. If $m$ equals $-\infty$, then the abundance conjecture predicts that $X$ is uniruled. In this case, every component of every degeneration is also uniruled, and thus has Kodaira dimension equal to $-\infty$. | |
| Jan 23, 2019 at 19:24 | comment | added | Evgeny Shinder | By the way, what about more general statement: if X has Kodaira dimension m, then every component of a degeneration of X has Kodaira dimension bounded by m? Is this false? | |
| Jan 23, 2019 at 19:19 | comment | added | Evgeny Shinder | One method to solve similar questions is using specialization map for the Grothendieck ring of varieties, as in arxiv.org/abs/1708.02790 and arxiv.org/abs/1708.05699v1. | |
| Jan 21, 2019 at 13:25 | comment | added | Ariyan Javanpeykar | I agree that the generic fibre is not uniruled. Assume it is uniruled. Take a general point on the special fiber $X_s$. Let $x\in X$ be a point specializing to this point. First, since $X_K$ is uniruled, there is a rational curve going through $x_K$. Second, this rational curve specializes to a rational curve through $x_s$. | |
| Jan 21, 2019 at 12:33 | comment | added | Jason Starr | The general fiber is non-uniruled. The abundance conjecture then predicts that the Kodaira dimension is nonnegative. | |
| Jan 21, 2019 at 7:49 | history | edited | Ariyan Javanpeykar | CC BY-SA 4.0 |
deleted 96 characters in body
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| S Jan 21, 2019 at 7:45 | history | bounty started | Ariyan Javanpeykar | ||
| S Jan 21, 2019 at 7:45 | history | notice added | Ariyan Javanpeykar | Authoritative reference needed | |
| Jan 18, 2019 at 15:59 | history | asked | Ariyan Javanpeykar | CC BY-SA 4.0 |