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...
Saved in:
| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2012 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2012
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/148409 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-148409 |
|---|---|
| record_format |
dspace |
| 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 |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Monodromy of an Inhomogeneous Picard-Fuchs Equation |
| spellingShingle |
Monodromy of an Inhomogeneous Picard-Fuchs Equation Laporte, G. Walcher, J. |
| title_short |
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_sort |
monodromy of an inhomogeneous picard-fuchs equation |
| author |
Laporte, G. Walcher, J. |
| author_facet |
Laporte, G. Walcher, J. |
| publishDate |
2012 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| 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.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/148409 |
| 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. |
| work_keys_str_mv |
AT laporteg monodromyofaninhomogeneouspicardfuchsequation AT walcherj monodromyofaninhomogeneouspicardfuchsequation |
| first_indexed |
2025-12-07T17:19:45Z |
| last_indexed |
2025-12-07T17:19:45Z |
| _version_ |
1850870842626408448 |