Back to Search
Start Over
Un exemple de feuilletage modulaire déduit d'une solution algébrique de l'équation de Painlevé VI
- Source :
- Annales de l'Institut Fourier, Annales de l'Institut Fourier, 2014, 64 (2), pp.699-737. ⟨10.5802/aif.2863⟩, Annales de l'Institut Fourier, Association des Annales de l'Institut Fourier, 2014, 64 (2), pp.699-737. 〈10.5802/aif.2863〉, Annales de l'Institut Fourier, Association des Annales de l'Institut Fourier, 2014, 64 (2), pp.699-737. ⟨10.5802/aif.2863⟩
- Publication Year :
- 2014
- Publisher :
- HAL CCSD, 2014.
-
Abstract
- One can easily give examples of rank 2 flat connections over $\mathbb{P}^2$ by rational pull-back of connections over $\mathbb{P}^1$. We give an example of a connection that can not occur in this way; this example is constructed from an algebraic solution of Painlev\'e VI equation. From this example we deduce a Hilbert modular foliation. The proof of this relies on the classification of foliations on projective surfaces due to Brunella, Mc Quillan and Mendes. Then, we get the dual foliation and, by a precise monodromy analysis, we see that our twice foliated surface is covered by the classical Hilbert modular surface constructed from the action of $\mathrm{PSL}_2(\mathbb{Z}[\sqrt{3}])$ on the bidisc.<br />Comment: 35 pages
- Subjects :
- Surface (mathematics)
Pure mathematics
[ MATH.MATH-CV ] Mathematics [math]/Complex Variables [math.CV]
Rank (differential topology)
01 natural sciences
surfaces modulaires de Hilbert
32S65
32C20
32C15
32S40
Mathematics - Algebraic Geometry
0103 physical sciences
0101 mathematics
Connection (algebraic framework)
Mathematics
feuilletages holomorphes
Algebra and Number Theory
équation de Painlevé VI
Mathematics - Complex Variables
Algebraic solution
010102 general mathematics
[MATH.MATH-CV]Mathematics [math]/Complex Variables [math.CV]
16. Peace & justice
connexions plates
[ MATH.MATH-AG ] Mathematics [math]/Algebraic Geometry [math.AG]
dimension de Kodaira
Monodromy
Foliation (geology)
Kodaira dimension
010307 mathematical physics
Geometry and Topology
[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]
Hilbert modular surface
Subjects
Details
- Language :
- French
- ISSN :
- 03730956 and 17775310
- Database :
- OpenAIRE
- Journal :
- Annales de l'Institut Fourier, Annales de l'Institut Fourier, 2014, 64 (2), pp.699-737. ⟨10.5802/aif.2863⟩, Annales de l'Institut Fourier, Association des Annales de l'Institut Fourier, 2014, 64 (2), pp.699-737. 〈10.5802/aif.2863〉, Annales de l'Institut Fourier, Association des Annales de l'Institut Fourier, 2014, 64 (2), pp.699-737. ⟨10.5802/aif.2863⟩
- Accession number :
- edsair.doi.dedup.....dc8b309839e1225663965e1a19a8241e