Mathematics – Algebraic Geometry
Scientific paper
2004-12-30
Mathematics
Algebraic Geometry
24 pages, 1 figure. Added computation of Euler characteristic and made some minor corrections
Scientific paper
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.
Enckevort Christian van
Straten Duco van
No associations
LandOfFree
Monodromy calculatons of fourth order equations of Calabi-Yau type does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Monodromy calculatons of fourth order equations of Calabi-Yau type, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Monodromy calculatons of fourth order equations of Calabi-Yau type will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-45724