Hermitian-holomorphic (2)-Gerbes and tame symbols
| dc.creator | Aldrovandi, Ettore | |
| dc.date | 2003-10-02 | |
| dc.date | 2004-10-13 | |
| dc.date.accessioned | 2026-07-07T06:26:24Z | |
| dc.date.available | 2026-07-07T06:26:24Z | |
| dc.description | We observe that the line bundle associated to the tame symbol of two invertible holomorphic functions also carries a fairly canonical hermitian metric, hence it represents a class in a Hermitian holomorphic Deligne cohomology group. We put forward an alternative definition of hermitian holomorphic structure on a gerbe which is closer to the familiar one for line bundles and does not rely on an explicit ``reduction of the structure group.'' Analogously to the case of holomorphic line bundles, a uniqueness property for the connective structure compatible with the hermitian-holomorphic structure on a gerbe is also proven. Similar results are proved for 2-gerbes as well. We then show the hermitian structures so defined propagate to a class of higher tame symbols previously considered by Brylinski and McLaughlin, which are thus found to carry corresponding hermitian-holomorphic structures. Therefore we obtain an alternative characterization for certain higher Hermitian holomorphic Deligne cohomology groups. | |
| dc.description | Sections on comparisons for hermitian connective structures added at referee's request. Some new results on compatibility between hermitian and analytic connective structures | |
| dc.identifier | https://arxiv.org/abs/math/0310027 | |
| dc.identifier | http://arxiv.org/abs/math/0310027 | |
| dc.identifier | Journal of Pure and Applied Algebra 200 (2005), 97--135 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/97095 | |
| dc.subject | Category Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Differential Geometry | |
| dc.subject | K-Theory and Homology | |
| dc.title | Hermitian-holomorphic (2)-Gerbes and tame symbols | |
| dc.type | text |