Calabi-Yau Manifolds Over Finite Fields, II
| dc.creator | Candelas, Philip | |
| dc.creator | de la Ossa, Xenia | |
| dc.creator | Rodriguez-Villegas, Fernando | |
| dc.date | 2004-02-17 | |
| dc.date.accessioned | 2026-07-07T04:16:38Z | |
| dc.date.available | 2026-07-07T04:16:38Z | |
| dc.description | We study zeta-functions for a one parameter family of quintic threefolds defined over finite fields and for their mirror manifolds and comment on their structure. The zeta-function for the quintic family involves factors that correspond to a certain pair of genus 4 Riemann curves. The appearance of these factors is intriguing since we have been unable to `see' these curves in the geometry of the quintic. Having these zeta-functions to hand we are led to comment on their form in the light of mirror symmetry. That some residue of mirror symmetry survives into the zeta-functions is suggested by an application of the Weil conjectures to Calabi-Yau threefolds: the zeta-functions are rational functions and the degrees of the numerators and denominators are exchanged between the zeta-functions for the manifold and its mirror. It is clear nevertheless that the zeta-function, as classically defined, makes an essential distinction between Kahler parameters and the coefficients of the defining polynomial. It is an interesting question whether there is a `quantum modification' of the zeta-function that restores the symmetry between the Kahler and complex structure parameters. We note that the zeta-function seems to manifest an arithmetic analogue of the large complex structure limit which involves 5-adic expansion. | |
| dc.description | Plain TeX, 50 pages, 4 eps figures | |
| dc.identifier | https://arxiv.org/abs/hep-th/0402133 | |
| dc.identifier | http://arxiv.org/abs/hep-th/0402133 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/52435 | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | Calabi-Yau Manifolds Over Finite Fields, II | |
| dc.type | text |