Timeline for Polarizations on intermediate Jacobians
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 2, 2010 at 14:01 | comment | added | Tony Pantev | If $X$ is a Kahler manifold which is projective, then any choice of an ample line bundle on $X$ induces a natural polarization on $J^{k}X$. This is a $(1,1)$ integral class on $J^{k}X$ which as a Hermitian pairing is non-degenerate but need not be definite. The corresponding holomorphic line bundle is non-degenerate and its powers have only one non-trivial cohomology group, namely the cohomology of degree the number of negative eigenvalues. The corresponding cohomology classes can be viewed as forms with coefficients in the line bundle. These are the analogues of the theta functions. | |
| Jun 1, 2010 at 16:09 | answer | added | Donu Arapura | timeline score: 4 | |
| Jun 1, 2010 at 16:06 | answer | added | Charles Siegel | timeline score: 2 | |
| Jun 1, 2010 at 15:43 | history | asked | Andrea Ferretti | CC BY-SA 2.5 |