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Monodromy of an Inhomogeneous Picard-Fuchs Equation
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2012, том 8
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Monodromy of an Inhomogeneous Picard-Fuchs Equation
Інший ID:
2010 Mathematics Subject Classification: 14C25; 14J33
DOI: http://dx.doi.org/10.3842/SIGMA.2012.056
DOI: http://dx.doi.org/10.3842/SIGMA.2012.056
Посилання:
Monodromy of an Inhomogeneous Picard-Fuchs Equation / G. Laporte, J. Walcher // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 10 назв. — англ.
Підтримка:
This paper is a contribution to the Special Issue “Mirror Symmetry and Related Topics”. The full collection is available at http://www.emis.de/journals/SIGMA/mirror symmetry.html.
We would like to thank Matt Kerr for asking the question addressed in this work, and Josh
Lapan for stimulating discussions. J.W. wishes to thank the Simons Center for Geometry and Physics, where this paper was written up. This work was supported in part by the Canada Research Chair program and an NSERC discovery grant.
Дата:
2012
Переглядів:
580
Завантажень:
235
Анотація:
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.
