Spin(7) instantons and the Hodge Conjecture for certain abelian four-folds: a modest proposal
| dc.creator | Ramakrishnan, Ramadas T. | |
| dc.date | 2008-09-23 | |
| dc.date.accessioned | 2026-07-07T10:04:41Z | |
| dc.date.available | 2026-07-07T10:04:41Z | |
| dc.description | The Hodge Conjecture is equivalent to a statement about conditions under which a complex vector bundle on a smooth complex projective variety admits a holomorphic structure. I advertise a class of abelian four-folds due to Mumford where this approach could be tested. I construct explicit smooth vector bundles - which can in fact be constructed in terms of of smooth line bundles - whose Chern characters are given Hodge classes. An instanton connection on these vector bundles would endow them with a holomorphic structure and thus prove that these classes are algebraic. I use complex multiplication to exhibit Cayley cycles representing the given Hodge classes. I find alternate complex structures with respect to which the given bundles are holomorphic, and close with a suggestion (due to G. Tian) as to how this may possibly be put to use. | |
| dc.description | 1 figure. A previous version was published as an ICTP preprint | |
| dc.identifier | https://arxiv.org/abs/0809.3927 | |
| dc.identifier | http://arxiv.org/abs/0809.3927 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/169767 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Differential Geometry | |
| dc.subject | 14C30;53C27 | |
| dc.title | Spin(7) instantons and the Hodge Conjecture for certain abelian four-folds: a modest proposal | |
| dc.type | text |