Monodromy of an Inhomogeneous Picard-Fuchs Equation

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 obt...

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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2012
Hauptverfasser: Laporte, G., Walcher, J.
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2012
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/148409
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Zitieren: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.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Laporte, G.
Walcher, J.
author_facet Laporte, G.
Walcher, J.
citation_txt 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.
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description 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.
first_indexed 2025-12-07T17:19:45Z
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2025-12-07T17:19:45Z
publishDate 2012
publisher Інститут математики НАН України
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spelling Laporte, G.
Walcher, J.
2019-02-18T11:50:17Z
2019-02-18T11:50:17Z
2012
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.
1815-0659
2010 Mathematics Subject Classification: 14C25; 14J33
DOI: http://dx.doi.org/10.3842/SIGMA.2012.056
https://nasplib.isofts.kiev.ua/handle/123456789/148409
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.
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.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Monodromy of an Inhomogeneous Picard-Fuchs Equation
Article
published earlier
spellingShingle Monodromy of an Inhomogeneous Picard-Fuchs Equation
Laporte, G.
Walcher, J.
title Monodromy of an Inhomogeneous Picard-Fuchs Equation
title_full Monodromy of an Inhomogeneous Picard-Fuchs Equation
title_fullStr Monodromy of an Inhomogeneous Picard-Fuchs Equation
title_full_unstemmed Monodromy of an Inhomogeneous Picard-Fuchs Equation
title_short Monodromy of an Inhomogeneous Picard-Fuchs Equation
title_sort monodromy of an inhomogeneous picard-fuchs equation
url https://nasplib.isofts.kiev.ua/handle/123456789/148409
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AT walcherj monodromyofaninhomogeneouspicardfuchsequation