Timeline for Grauert's criteria for ample line bundles
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Sep 23, 2011 at 13:58 | comment | added | Jun Li | Thank you for the advise and the vacubulary.It seems wonderful and I will have a try. | |
| Sep 22, 2011 at 20:35 | comment | added | roy smith | verschwinden = vanishes, schnittfla"che = section, keine = no, Menge = set, Teilmenge = subset, Garbe = sheaf, Geradenbundel = line bundle, Jede = any, fortsetzen =(?) extends, and you can guess: exakte Sequenz = .... | |
| Sep 22, 2011 at 20:26 | comment | added | roy smith | even if you think you don't read german, you might try Grauert's paper, in pretty clear german, from middle page 347 to top 349. he uses induction, finds X1, the zero set in X of a section of a power of F, then applies induction to the restriction of F to X1. If Kleiman uses the same argument you might read them together. Grauert uses Remmert's reduction theorem which allows one to blow down compact subvarieties of a holom convex space to a Stein space, with the structure sheaf also pushing down. gdz.sub.uni-goettingen.de/en/dms/load/img | |
| Sep 21, 2011 at 15:12 | comment | added | Damian Rössler | Another reference in the algebraic situation is P. Cartier, Diviseurs amples. Séminaire Bourbaki, Vol. 9, Exp. No. 301, 351–366, Soc. Math. France, Paris, 1995. archive.numdam.org/ARCHIVE/SB/SB_1964-1966__9_/… | |
| Sep 21, 2011 at 12:02 | comment | added | Jun Li | The reference is very helpful.Thank you. | |
| Sep 21, 2011 at 9:16 | comment | added | Francesco Polizzi | I had a (quick) look at the proof and it seems to me that it should extend without problems to the compact analytic setting. | |
| Sep 21, 2011 at 8:55 | comment | added | Ben McKay | Kleiman states that his proof is for complete algebraic schemes. Does it work verbatim for compact analytic spaces? | |
| Sep 21, 2011 at 8:40 | history | answered | Francesco Polizzi | CC BY-SA 3.0 |