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

This article is cited in 6 scientific papers (total in 6 papers)

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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Full text: http://emis.mi.ras.ru/.../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.

Citation in format AMSBIB
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\by Guillaume Laporte, Johannes Walcher
\paper Monodromy of an inhomogeneous Picard--Fuchs equation
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\vol 8
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    Citing articles on Google Scholar: Russian citations, English citations
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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  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    2. Jefferson R.A., Walcher J., “Monodromy of Inhomogeneous Picard-Fuchs Equations”, Commun. Number Theory Phys., 8:1 (2014), 1–40  crossref  mathscinet  zmath  isi  scopus
    3. Doran Ch.F., Kerr M., “Algebraic Cycles and Local Quantum Cohomology”, Commun. Number Theory Phys., 8:4 (2014), 703–727  crossref  mathscinet  zmath  isi  scopus
    4. Kerr, M., “Algebraic and arithmetic properties of period maps”, Fields Institute Monographs, 34 (2015), 173-208  crossref  mathscinet  zmath  scopus
    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  crossref  mathscinet  isi  scopus
    6. Honma Y., Manabe M., “Open mirror symmetry for higher dimensional Calabi-Yau hypersurfaces”, J. High Energy Phys., 2016, no. 3, 160  crossref  mathscinet  zmath  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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