Monodromy calculatons of fourth order equations of Calabi-Yau type
| dc.creator | van Enckevort, Christian | |
| dc.creator | van Straten, Duco | |
| dc.date | 2004-12-30 | |
| dc.date | 2005-03-20 | |
| dc.date.accessioned | 2026-07-07T05:15:42Z | |
| dc.date.available | 2026-07-07T05:15:42Z | |
| dc.description | This paper contains a preliminary study of the monodromy of certain fourth order differential equations, that were called of Calabi-Yau type in math.NT/0402386. Some of these equations can be interpreted as the Picard-Fuchs equations of a Calabi-Yau manifold with one complex modulus, which links up the observed integrality to the conjectured integrality of the Gopakumar-Vafa invariants. A natural question is if in the other cases such a geometrical interpretation is also possible. Our investigations of the monodromies are intended as a first step in answering this question. We use a numerical approach combined with some ideas from homological mirror symmetry to determine the monodromy for some further one-parameter models. Furthermore, we present a conjectural identification of the Picard-Fuchs equation for 5 new examples from Borcea's list and one constructed by Tonoli and conjecture the existence of some new Calabi-Yau three folds. The paper does not contain any theorems or proofs but is, we think, nevertheless of interest. | |
| dc.description | 24 pages, 1 figure. Added computation of Euler characteristic and made some minor corrections | |
| dc.identifier | https://arxiv.org/abs/math/0412539 | |
| dc.identifier | http://arxiv.org/abs/math/0412539 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73721 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Number Theory | |
| dc.subject | 14J32 (Primary) 32S40, 81T30 (Secondary) | |
| dc.title | Monodromy calculatons of fourth order equations of Calabi-Yau type | |
| dc.type | text |