Timeline for Existence of a non-degenerate global section is an open property?
Current License: CC BY-SA 4.0
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| May 25, 2020 at 16:38 | history | edited | Walter field | CC BY-SA 4.0 |
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| May 25, 2020 at 16:23 | comment | added | R. van Dobben de Bruyn | By upper semicontinuity, a much more plausible question would be the opposite: if $E_t$ does not have a [insert adjective] section, then does the same hold in a neighbourhood? | |
| May 25, 2020 at 16:14 | comment | added | R. van Dobben de Bruyn | What if you take the family of $\mathscr L \oplus \mathscr L$ where $\mathscr L$ runs over all degree $0$ line bundles of a curve (or surface if you insist that $X$ is a surface)? Then the trivial line bundle has such a section, but the others don't have any nonzero global sections. | |
| May 25, 2020 at 16:12 | comment | added | Walter field | Sorry.I added the definition of non-degenerate global section. | |
| May 25, 2020 at 16:11 | history | edited | Walter field | CC BY-SA 4.0 |
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| May 25, 2020 at 16:05 | history | edited | Walter field | CC BY-SA 4.0 |
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| May 25, 2020 at 15:58 | comment | added | Mohan | What does non-degenerate global section mean to you? | |
| May 25, 2020 at 15:33 | history | asked | Walter field | CC BY-SA 4.0 |