Hermitian-holomorphic Deligne cohomology, Deligne pairing for singular metrics, and hyperbolic metrics
| dc.creator | Aldrovandi, Ettore | |
| dc.date | 2004-08-09 | |
| dc.date | 2004-08-13 | |
| dc.date.accessioned | 2026-07-07T06:26:24Z | |
| dc.date.available | 2026-07-07T06:26:24Z | |
| dc.description | We introduce a model for Hermitian holormorphic Deligne cohomology on a projective algebraic manifold which allows to incorporate singular hermitian structures along a normal crossing divisor. In the case of a projective curve, the cup-product in cohomology is shown to correspond to a generalization of the Deligne pairing to line bundles with "good" hermitian metrics in the sense of Mumford and others. A particular case is that of the tangent bundle of the curve twisted by the negative of the singularity divisor of a hyperbolic metric: its cup square (corrected by the total area) is shown to be a functional whose extrema are the metrics of constant negative curvature. | |
| dc.description | LaTeX + amsmath + mathrsfs + textcomp. 21 pages, no figures Added one clarifying lemma at the end, no changes to the main results | |
| dc.identifier | https://arxiv.org/abs/math/0408118 | |
| dc.identifier | http://arxiv.org/abs/math/0408118 | |
| dc.identifier | Int. Mathematics Research Notices 17 (2005), 1015--1046 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/97096 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Complex Variables | |
| dc.subject | Differential Geometry | |
| dc.title | Hermitian-holomorphic Deligne cohomology, Deligne pairing for singular metrics, and hyperbolic metrics | |
| dc.type | text |