Monodromy calculatons of fourth order equations of Calabi-Yau type

dc.creatorvan Enckevort, Christian
dc.creatorvan Straten, Duco
dc.date2004-12-30
dc.date2005-03-20
dc.date.accessioned2026-07-07T05:15:42Z
dc.date.available2026-07-07T05:15:42Z
dc.descriptionThis 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.description24 pages, 1 figure. Added computation of Euler characteristic and made some minor corrections
dc.identifierhttps://arxiv.org/abs/math/0412539
dc.identifierhttp://arxiv.org/abs/math/0412539
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/73721
dc.subjectAlgebraic Geometry
dc.subjectNumber Theory
dc.subject14J32 (Primary) 32S40, 81T30 (Secondary)
dc.titleMonodromy calculatons of fourth order equations of Calabi-Yau type
dc.typetext

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