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 SIGMA, 2012, Volume 8, 056, 10 pages (Mi sigma733)

Monodromy of an inhomogeneous Picard–Fuchs equation

Guillaume Laportea, Johannes Walcherab

a Department of Physics, McGill University, Montréal, Québec, Canada
b Department of Mathematics and Statistics, McGill University, Montréal, Québec, Canada

Abstract: The global behaviour of the normal function associated with van Geemen's family of lines on the mirror quintic is studied. Based on the associated inhomogeneous Picard–Fuchs equation, the series expansions around large complex structure, conifold, and around the open string discriminant are obtained. The monodromies are explicitly calculated from this data and checked to be integral. The limiting value of the normal function at large complex structure is an irrational number expressible in terms of the di-logarithm.

Keywords: algebraic cycles, mirror symmetry, quintic threefold.

DOI: https://doi.org/10.3842/SIGMA.2012.056

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ArXiv: 1206.1787
MSC: 14C25; 14J33
Received: June 8, 2012; in final form August 20, 2012; Published online August 22, 2012
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Citation: Guillaume Laporte, Johannes Walcher, “Monodromy of an inhomogeneous Picard–Fuchs equation”, SIGMA, 8 (2012), 056, 10 pp.

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\Bibitem{LapWal12} \by Guillaume Laporte, Johannes Walcher \paper Monodromy of an inhomogeneous Picard--Fuchs equation \jour SIGMA \yr 2012 \vol 8 \papernumber 056 \totalpages 10 \mathnet{http://mi.mathnet.ru/sigma733} \crossref{https://doi.org/10.3842/SIGMA.2012.056} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2970772} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000307830000001} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84865813571} 

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This publication is cited in the following articles:
1. Adams L., Bogner Ch., Weinzierl S., “The Two-Loop Sunrise Graph with Arbitrary Masses”, J. Math. Phys., 54:5 (2013), 052303
2. Jefferson R.A., Walcher J., “Monodromy of Inhomogeneous Picard-Fuchs Equations”, Commun. Number Theory Phys., 8:1 (2014), 1–40
3. Doran Ch.F., Kerr M., “Algebraic Cycles and Local Quantum Cohomology”, Commun. Number Theory Phys., 8:4 (2014), 703–727
4. Kerr, M., “Algebraic and arithmetic properties of period maps”, Fields Institute Monographs, 34 (2015), 173-208
5. Zou H., Yang F.-Zh., “Effective superpotentials of Type II D-brane/F-theory on compact complete intersection Calabi–Yau threefolds”, Mod. Phys. Lett. A, 31:15 (2016), 1050094
6. Honma Y., Manabe M., “Open mirror symmetry for higher dimensional Calabi-Yau hypersurfaces”, J. High Energy Phys., 2016, no. 3, 160
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