Timeline for Algebraic geometry used "externally" (in problems without obvious algebraic structure).
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 28, 2010 at 21:31 | comment | added | Allen Knutson | @Victor: when the facets are simplices (as assumed above), you can wiggle the vertices a little bit without changing the combinatorics. | |
| Jun 28, 2010 at 7:50 | comment | added | Torsten Ekedahl | I thought that the proof of the strong Lefschetz for combinatorially defined intersection cohomology was proven by a reduction to the simplicial case which in turn reduces to the rational case. Hence the proof is not independent of algebraic geometry. | |
| Jun 28, 2010 at 6:45 | comment | added | Victor Protsak | To be completely honest, the toric proof only works for $\textit{rational}$ convex polytopes (which seems like totally insignificant technicality until you learn that there are non-rational polytopes not combinatorially equivalent to any rational ones), whereas combinatorial intersection cohomology, although certainly inspired by it, works in complete generality. | |
| Jun 25, 2010 at 18:11 | comment | added | Torsten Ekedahl | Could you give a reference for the combinatorial proof? (I didn't know about that.) | |
| Jun 24, 2010 at 9:04 | comment | added | Martin Brandenburg | I agree. This should also be a nice motivation for starting to learn algebraic geometry (or at least toric geometry). | |
| Jun 23, 2010 at 22:19 | comment | added | Daniel Litt | Wow! This is amazing. | |
| Jun 23, 2010 at 22:16 | history | answered | Allen Knutson | CC BY-SA 2.5 |