Timeline for Clemens-Griffiths component birational invariant
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Jun 28, 2020 at 23:06 | comment | added | Evgeny Shinder | An excellent modern survey by Beauville: arxiv.org/pdf/1507.02476.pdf; see section 3 for the intermediate Jacobian. | |
| Jun 25, 2020 at 19:22 | comment | added | abx | In Clemens-Griffiths of course. | |
| Jun 25, 2020 at 17:21 | comment | added | user267839 | @abx: where can I find a proof of this fact you have quoted. | |
| Jun 25, 2020 at 17:17 | history | edited | user267839 | CC BY-SA 4.0 |
added 53 characters in body
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| Jun 25, 2020 at 16:35 | comment | added | Enrico | At the level of intuition --so a very sloppy comment (I assume that we are speaking about threefolds here). Suppose you take a (say) smooth threefold and you want to blow it up in a (say) smooth curve. $H^{2,1}(X)$ will not tell you much about the curve you are blowing up (just its genus). However, if you quotient out by $H^3(X, \mathbb{Z})$ then you want to recover the Jacobian of curve, which by Torelli determines the curve up to isomorphism (and smooth projective birational curves are isomorphic). Do not take it as a complete answer, but I found this picture helpful back in the days. | |
| Jun 25, 2020 at 16:33 | comment | added | abx | The geometry is that when you blow up a curve in a threefold, you modify the intermediate Jacobian by adding the Jacobian of the curve. This seems pretty geometric to me. | |
| Jun 25, 2020 at 15:32 | history | asked | user267839 | CC BY-SA 4.0 |