Timeline for Are rationally connected varieties uniruled?
Current License: CC BY-SA 3.0
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| Sep 24, 2013 at 16:04 | comment | added | Vesselin Dimitrov | Yes, this is the difference between inseparable and separable rational connectivity (which only arises in positive characteristic, of course). The proposition remains true upon adding the qualifier "separably" in front of "uniruled" and "rationally connected"; this is Theorems IV 1.9 and IV 3.7 in Kollar's book. The example you give is not separably uniruled. | |
| Sep 24, 2013 at 15:11 | comment | added | Francesco Polizzi | You are right. It is the characterization by using free rational curves that only holds in characteristic zero. I corrected the answer and added a remark, thank you for the observation. | |
| Sep 24, 2013 at 15:09 | history | edited | Francesco Polizzi | CC BY-SA 3.0 |
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| Sep 24, 2013 at 14:52 | comment | added | Vesselin Dimitrov | But why do you write "in characteristic zero?" Over any uncountable field, uniruledness simply means that there is a rational curve through any general point; rational connectivity is in turn the stronger property that there is a rational curve through any two general points. | |
| Aug 25, 2013 at 12:15 | history | edited | Francesco Polizzi | CC BY-SA 3.0 |
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| Aug 25, 2013 at 12:08 | history | answered | Francesco Polizzi | CC BY-SA 3.0 |