Timeline for Do line bundles with enough sections on surfaces have generic divisors which are irreducible?
Current License: CC BY-SA 4.0
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| Jul 13, 2018 at 3:01 | comment | added | Mohan | @Kim No, all the sections of $L^2$ comes from $\mathbb{P}^1$ and so no divisor in this system would be irreducible, since any section of $\mathcal{O}_{\mathbb{P}^1}(2)$ vanishes at two points, counted with multiplicity. | |
| Jul 13, 2018 at 1:47 | vote | accept | Kim | ||
| Jul 13, 2018 at 1:35 | comment | added | Kim | Thanks for the example. Do you think it may have a chance of holding for the elliptic fibration case above? | |
| Jul 13, 2018 at 0:01 | history | answered | Mohan | CC BY-SA 4.0 |