Timeline for Determinant and exact sequences of sheaves.
Current License: CC BY-SA 2.5
9 events
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| Feb 4, 2011 at 16:46 | comment | added | Mohan | There are two issues with your question. First of all, there is no natural map of $\det E\to\det G$ given your exact sequence. The only natural map is $\det E\otimes \mathcal{O}(D)\to\det G$. Secondly, if you had an exact sequence of determinants as you mention (possibly unnatural), it forces $\det E=\det G(-D)$. This need not be true in general. For example, let $M$ be an effective divisor and let $G=E(M)\oplus \mathcal{O}$ and the map being $E\to E(M)$. Then the double dual of $H$ is trivial and $\det E\neq \det G$. | |
| Feb 4, 2011 at 15:52 | vote | accept | ginevra86 | ||
| Feb 4, 2011 at 15:36 | answer | added | inkspot | timeline score: 3 | |
| Feb 4, 2011 at 15:11 | answer | added | Mike Skirvin | timeline score: 1 | |
| Feb 4, 2011 at 13:50 | answer | added | AFK | timeline score: 0 | |
| Feb 4, 2011 at 13:44 | history | edited | Francesco Polizzi | CC BY-SA 2.5 |
added 1 characters in body; edited title
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| Feb 4, 2011 at 13:44 | history | edited | ginevra86 | CC BY-SA 2.5 |
deleted 10 characters in body
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| Feb 4, 2011 at 13:43 | history | edited | Francesco Polizzi | CC BY-SA 2.5 |
edited body
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| Feb 4, 2011 at 13:40 | history | asked | ginevra86 | CC BY-SA 2.5 |