
SIGMA 8 (2012), 056, 10 pages arXiv:1206.1787
https://doi.org/10.3842/SIGMA.2012.056
Contribution to the Special Issue “Mirror Symmetry and Related Topics”
Monodromy of an Inhomogeneous PicardFuchs Equation
Guillaume Laporte ^{a} and Johannes Walcher ^{a, b}
^{a)} Department of Physics, McGill University, Montréal, Québec, Canada
^{b)} Department of Mathematics and Statistics, McGill University, Montréal, Québec, Canada
Received June 08, 2012, in final form August 20, 2012; Published online August 22, 2012
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 PicardFuchs 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 dilogarithm.
Key words:
algebraic cycles; mirror symmetry; quintic threefold.
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