Timeline for Examples of nontrivial morphism between simple bundles but not isomorphism
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| yesterday | comment | added | afh | Let $X$ be a smooth projective curve of genus 2, and let $L,M$ be two nonisomorphic line bundles of degree zero. Consider nontrivial extensions $L\to E \to M$ and $M \to E' \to L$ (these exists by the nonvanishing of the corresponding Ext groups, which can be seen using Riemann Roch). Then I believe that both $E$ and $E'$ are simple rank 2 bundles of degree 0, but the composition $E\to M \to E'$ is a nonzero morphism which is not an isomorphism. | |
| yesterday | history | edited | Z. Liu | CC BY-SA 4.0 |
added 9 characters in body
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| S yesterday | review | First questions | |||
| yesterday | |||||
| S yesterday | history | asked | Z. Liu | CC BY-SA 4.0 |