Timeline for Example of variety which is not a complete intersection with respect to any projective embedding
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 17, 2018 at 20:00 | comment | added | Yemon Choi | Perhaps one of the commenters would like to leave an answer below? | |
| Nov 14, 2018 at 16:50 | comment | added | Mohan Swaminathan | Thanks for all the comments, this answers my question. | |
| Nov 14, 2018 at 16:35 | review | Close votes | |||
| Nov 17, 2018 at 20:00 | |||||
| Nov 14, 2018 at 16:18 | comment | added | R. van Dobben de Bruyn | Complete intersections are a very special class of varieties. The Lefschetz hyperplane theorem gives strong restrictions on the cohomology of a complete intersection. | |
| Nov 14, 2018 at 16:15 | comment | added | Jonathan Frink | Also a hyperelliptic curve of any genus $\ge 2$ works, since the canonical bundle of a complete intersection curve would be (very) ample. | |
| Nov 14, 2018 at 16:11 | comment | added | Jonathan Frink | A smooth variety of dimension $\ge 2$ which is a complete intersection must be simply connected by the Lefschetz hyperplane theorem, so you get lots of counterexamples (e.g., for abelian varieties). | |
| Nov 14, 2018 at 16:09 | comment | added | pbelmans | Curves of many genera are not realisable as complete intersections, see mathoverflow.net/questions/179688/…. | |
| Nov 14, 2018 at 16:06 | history | asked | Mohan Swaminathan | CC BY-SA 4.0 |