Timeline for construct the elliptic fibration of elliptic k3 surface
Current License: CC BY-SA 3.0
12 events
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| Feb 3, 2022 at 0:16 | comment | added | John Baez | I think @AmorFati and diveritti mean different things when they say "the curve". The fibers of the elliptic fibration are generically curves of genus 1, and such curves indeed have nonzero holomorphic 1-forms, but diverietti's original claim was that the base space $C$ must be a curve of genus 0, because the total space $S$ has no nonzero holomorphic 1-forms. | |
| Aug 24, 2020 at 13:03 | comment | added | diverietti | I don't understand. The general fibre has genus one, indeed. | |
| Aug 21, 2020 at 1:05 | comment | added | AmorFati | @diverietti Why is the curve not allowed to have genus $1$? The canonical bundle of an elliptic curve is trivial, so all the holomorphic forms on it are constant... | |
| Nov 13, 2013 at 18:54 | comment | added | Sándor Kovács | @Jay: regarding sections, look at my answer below. | |
| Jun 26, 2013 at 11:58 | history | edited | diverietti | CC BY-SA 3.0 |
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| Feb 8, 2012 at 5:11 | comment | added | Jay | that is great~ thanks! by the way, do you know anything about the existence of sections? maybe just a topological section... | |
| Feb 8, 2012 at 5:09 | vote | accept | Jay | ||
| Feb 7, 2012 at 9:40 | comment | added | diverietti | Good! So is this answer satisfactory or you wanted to know more specific things? | |
| Feb 6, 2012 at 12:42 | history | edited | diverietti | CC BY-SA 3.0 |
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| Feb 6, 2012 at 12:28 | history | edited | diverietti | CC BY-SA 3.0 |
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| Feb 6, 2012 at 11:23 | history | edited | diverietti | CC BY-SA 3.0 |
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| Feb 6, 2012 at 11:09 | history | answered | diverietti | CC BY-SA 3.0 |