Timeline for What properties of line bundles can be detected cohomologically?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Jul 22, 2017 at 2:51 | comment | added | user21574 | Assume that the curvature current $c(L,h) $ is smooth on the complement of some proper analytic subset$ Z$ of $X$ and that $c(L,h)$ is strictly positive on some tubular neighborhood $B$ of $Z$. Then $∫_{X_{reg}(≤1,L)}c(L,h)^n$ exists. If in addition this integral is positive, then $L$ is big, and in particular,$ X$ is a Moishezon space | |
| Jul 22, 2017 at 2:44 | comment | added | user21574 | Dan Popovici, Regularization of currents with mass control and singular Morse inequalities, J. Differential Geom. Volume 80, Number 2 (2008), 281-326. | |
| Jul 22, 2017 at 2:43 | comment | added | user21574 | I give Dan Popovici's characterization of big line bundle: Any almost positive current $T$ admits a Lebesgue decomposition into the sum of an absolutely continuous part $T_{ac}$ and a singular part. By taking the supremum over all $T$ in the Chern class of $L$ of the mass of the n-th exterior power of $T_{ac}$. Bigness of $L$ is then equivalent to existence of a possibly singular metric $h$ for which the curvature current is non-negative and its absolutely continuous part has positive n-mass. | |
| Jul 1, 2014 at 8:47 | answer | added | abx | timeline score: 5 | |
| Jul 1, 2014 at 4:44 | history | asked | Eric Canton | CC BY-SA 3.0 |