Timeline for Sheaves on families of genus 2 curves in Hassett's paper
Current License: CC BY-SA 4.0
4 events
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| Mar 10, 2022 at 15:54 | history | edited | Will Sawin | CC BY-SA 4.0 |
added 100 characters in body
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| Mar 10, 2022 at 15:53 | comment | added | Will Sawin | @gigi There's a number of ways to see it. One is Riemann-Roch, working fiber by fiber (so assume the base $S$ is a point). We know $H^1 ( \mathbb P, j_* \mathcal O_C) = H^1 ( C, \mathcal O_C) $ is a two-dimensional vector space and $H^1(\mathbb P, \mathcal O_{\mathbb P})=0$ so it all has to come from $\mathcal L$, which forces $\deg \mathcal L=-3$. | |
| Mar 10, 2022 at 15:37 | comment | added | gigi | Thank you very much! Now it's very clear. Do you know why the type of splitting is exactly the trivial line bundle sum with a line bundle of degree -3 on the fibers? | |
| Mar 10, 2022 at 15:06 | history | answered | Will Sawin | CC BY-SA 4.0 |