D. Abramovich and A. Vistoli, Compactifying the space of stable maps, Journal of the American Mathematical Society, vol.15, issue.01, pp.27-75, 2002.
DOI : 10.1090/S0894-0347-01-00380-0

D. Allcock, J. Carlson, and D. Toledo, Orthogonal complex hyperplane arrangements, Contemp. Math, pp.312-313, 2000.

J. Amorós and I. Bauer, On the number of defining relations for nonfibered Kähler groups, Internat. J. Math, vol.11, pp.285-290, 2000.

J. Amorós, M. Burger, K. Corlette, D. Kotschick, and D. Toledo, Fundamental groups of compact Kähler manifolds, A.M.S. Mathematical Surveys and Monographs, p.44, 1996.

D. Arapura, Geometry of cohomology support loci for local systems, I. J. Algebraic Geom, vol.6, pp.563-597, 1997.

D. Arapura, P. Bressler, and M. Ramachandran, On the fundamental group of a compact Kähler manifold. Duke Math, J, vol.68, pp.477-488, 1992.

V. Balaji, I. Biswas, and D. Nagaraj, Principal bundles over projective manifolds with parabolic structure over a divisor, Tohoku Mathematical Journal, vol.53, issue.3, pp.337-367, 2001.
DOI : 10.2748/tmj/1178207416

H. Bass, Groups of integral representation type, Pacific Journal of Mathematics, vol.86, issue.1, pp.15-51, 1980.
DOI : 10.2140/pjm.1980.86.15

A. Beauville, Annulation du H1 pour les fibr??s en droites plats, Complex algebraic varieties Lecture Notes in Math, vol.65, pp.1-15, 1990.
DOI : 10.1007/BF02566608

K. Behrend and B. Noohi, Uniformization of Deligne-Mumford curves, Journal f??r die reine und angewandte Mathematik (Crelles Journal), vol.2006, issue.599
DOI : 10.1515/CRELLE.2006.080

S. Bell, The Bergman kernel function and proper holomorphic mappings, Transactions of the American Mathematical Society, vol.270, issue.2, pp.685-691, 1982.
DOI : 10.1090/S0002-9947-1982-0645338-1

B. B. Hamed and L. Gavrilov, Families of Painleve VI equations having a common solution, Int. Math. Res. Not, vol.60, pp.3727-3752, 2005.

I. Biswas, Parabolic bundles as orbifold bundles, Duke Math, J, vol.88, pp.305-325, 1997.

O. Biquard, Sur Les Fibr??s Paraboliques Sur Une Surface Complexe, Journal of the London Mathematical Society, vol.53, issue.2, pp.302-316, 1996.
DOI : 10.1112/jlms/53.2.302

P. Boalch, From Klein to Painlev?? via Fourier, Laplace and Jimbo, Proc. London Math. Soc. 90, pp.167-208, 2005.
DOI : 10.1112/S0024611504015011

H. Boden and K. Yokogawa, Moduli spaces of parabolic Higgs bundles and parabolic K(D) pairs over smooth curves, I. Internat, J. Math, vol.7, pp.573-598, 1996.

F. Bogomolov and L. Katzarkov, Complex projective surfaces and infinite groups, Geometric And Functional Analysis, vol.8, issue.2, pp.243-272, 1998.
DOI : 10.1007/s000390050055

L. Breen, On the classification of 2-gerbes and 2-stacks, Astérisque, vol.225, 1994.

F. Campana, Remarques sur le rev??tement universel des vari??t??s k??hl??riennes compactes, Bulletin de la Société mathématique de France, vol.122, issue.2, pp.255-284, 1994.
DOI : 10.24033/bsmf.2232

F. Campana, Orbifoldes, vari??t??s sp??ciales et th??orie de la classification, Annales de l???institut Fourier, vol.54, issue.3, pp.499-630, 2004.
DOI : 10.5802/aif.2027

V. Caselles, G. Sapiro, A. Solé, and C. Ballester, Morse Description and Morphological Encoding of Continuous Data, Multiscale Modeling & Simulation, vol.2, issue.2, pp.179-209, 2004.
DOI : 10.1137/S1540345902416557

F. Catanese, Fundamental groups with few relations. Higher Dimensional Complex Varieties, pp.163-165, 1994.

E. Cattani, A. Kaplan, and W. Schmid, L 2 and intersection cohomologies for a polarizable variation of Hodge structure, Inventiones Mathematicae, vol.70, issue.2, pp.217-252, 1987.
DOI : 10.1007/BF01389415

D. Cohen and P. Orlik, Arrangements and local systems, Mathematical Research Letters, vol.7, issue.3, pp.299-316, 2000.
DOI : 10.4310/MRL.2000.v7.n3.a5

K. Cole-mclaughlin, H. Edelsbrunner, J. Harer, V. Natarajan, and V. Pascucci, Loops in Reeb graphs of 2-manifolds, Discrete Comput. Geom, vol.32, pp.231-244, 2004.

K. Corlette, Flat $G$-bundles with canonical metrics, Journal of Differential Geometry, vol.28, issue.3, pp.361-382, 1988.
DOI : 10.4310/jdg/1214442469

K. Corlette, Nonabelian Hodge theory and square integrability Actes du Colloque, Géométrie et Topologie des Variétés Projectives, 1992.

K. Corlette, Rigid representations of K??hlerian fundamental groups, Journal of Differential Geometry, vol.33, issue.1, pp.239-252, 1991.
DOI : 10.4310/jdg/1214446037

M. Culler and P. Shalen, Varieties of Group Representations and Splittings of 3-Manifolds, The Annals of Mathematics, vol.117, issue.1, pp.109-146, 1983.
DOI : 10.2307/2006973

H. Darmon, Rigid local systems, Hilbert modular forms, and Fermat's last theorem. Duke Math, J, vol.102, pp.413-449, 2000.

P. Deligne, Travaux de Shimura Séminaire Bourbaki, 389 Springer Lecture Notes in Math, pp.123-165, 1970.

P. Deligne, Variétés de Shimura: interprétation modulaire, et techniques de construction de modèles canoniques Automorphic forms, representations and L-functions (Corvallis, AMS Proc. Sympos. Pure Math, pp.247-289, 1977.

P. Deligne and G. Mostow, Monodromy of hypergeometric functions and non-lattice integral monodromy, Publications math??matiques de l'IH??S, vol.109, issue.1, pp.5-89, 1986.
DOI : 10.1007/BF02831622

P. Deligne and D. Mumford, The irreducibility of the space of curves of given genus, Publications math??matiques de l'IH??S, vol.44, issue.1, pp.75-109, 1969.
DOI : 10.1007/BF02684599

T. Delzant, L'invariant de Bieri Neumann Strebel des groupes fondamentaux des varietes kaehleriennes

T. Delzant, Trees, Valuations and the Green???Lazarsfeld Set, Geometric and Functional Analysis, vol.18, issue.4
DOI : 10.1007/s00039-008-0679-2
URL : https://hal.archives-ouvertes.fr/hal-00131474

M. Dettweiler and S. Reiter, An Algorithm of Katz and its Application to the Inverse Galois Problem, Journal of Symbolic Computation, vol.30, issue.6, pp.761-798, 2000.
DOI : 10.1006/jsco.2000.0382

K. Diederich and T. Ohsawa, Harmonic mappings and disc bundles over compact K??hler manifolds, Publications of the Research Institute for Mathematical Sciences, vol.21, issue.4, pp.819-833, 1985.
DOI : 10.2977/prims/1195178932

A. Dimca, Pencils of Plane Curves and Characteristic Varieties
DOI : 10.1007/978-3-0346-0209-9_3

A. Dimca and A. Nemethi, On the monodromy of complex polynomials. Duke Math, J, vol.108, pp.199-209, 2001.

S. Donaldson, Anti Self-Dual Yang-Mills Connections Over Complex Algebraic Surfaces and Stable Vector Bundles, Proceedings of the London Mathematical Society, vol.3, issue.1, pp.1-26, 1985.
DOI : 10.1112/plms/s3-50.1.1

S. Donaldson, Twisted Harmonic Maps and the Self-Duality Equations, Proc. London Math, pp.127-131, 1987.
DOI : 10.1112/plms/s3-55.1.127

B. Dubrovin, Geometry of 2D topological field theories Integrable systems and quantum groups (Montecatini Terme, 1993) Lecture Notes in Math, pp.1620-120, 1996.

J. Eells and J. Sampson, Harmonic Mappings of Riemannian Manifolds, American Journal of Mathematics, vol.86, issue.1, pp.109-160, 1964.
DOI : 10.2307/2373037

M. Entov and L. Polterovich, Calabi quasimorphism and quantum homology, Int. Math. Res. Not, vol.30, pp.1635-1676, 2003.

P. Eyssidieux, Sur la convexit??? holomorphe des rev???tements lin???aires r???ductifs d?une vari???t??? projective alg???brique complexe, Inventiones Mathematicae, vol.156, issue.3, pp.503-564, 2004.
DOI : 10.1007/s00222-003-0345-0

M. Falk and S. Yuzvinsky, Multinets, resonance varieties, and pencils of plane curves, Compositio Mathematica, vol.143, issue.04
DOI : 10.1112/S0010437X07002722

R. Friedman and J. Morgan, Donaldson and Seiberg-Witten invariants of algebraic surfaces, J. Algebraic Geom, vol.6, pp.445-479, 1997.
DOI : 10.1090/pspum/062.1/1492519

E. Freitag, Hilbert modular forms, 1990.

T. Gelander, A. Karlsson, and G. Margulis, Superrigidity, Generalized Harmonic Maps and Uniformly Convex Spaces, Geometric and Functional Analysis, vol.17, issue.5
DOI : 10.1007/s00039-007-0639-2

E. Goren, Lectures on Hilbert modular varieties and modular forms. With the assistance of Marc- Hubert Nicole, CRM Monograph Series, p.14, 2002.

M. Green and P. Griffiths, Hodge-theoretic invariants for algebraic cycles, Int. Math. Res. Not, vol.9, pp.477-510, 2003.

M. Gromov, Sur le groupe fondamental d'une variété kählérienne, C. R. Acad. Sci. Paris Sér. I Math, vol.308, pp.67-70, 1989.

M. Gromov and R. Schoen, Harmonic maps into singular spaces andp-adic superrigidity for lattices in groups of rank one, Publications math??matiques de l'IH??S, vol.1, issue.2, pp.165-246, 1992.
DOI : 10.1007/BF02699433

R. Hain, Finiteness and Torelli Spaces. Problems on mapping class groups and related topics, Proc. Sympos. Pure Math, pp.57-70, 2006.

N. Hitchin, Poncelet polygons and the Painlevé equations Geometry and analysis (Bombay, 1992) Tata Inst, Fund. Res, pp.151-185, 1995.

F. Hirzebruch and A. Van-de-ven, Hilbert modular surfaces and the classification of algebraic surfaces, Inventiones mathematicae, vol.92, issue.1, pp.1-29, 1974.
DOI : 10.1007/BF01405200

M. Inaba, K. Iwasaki, and M. Saito, Moduli of Stable Parabolic Connections, Riemann-Hilbert Correspondence and Geometry of Painlev?? Equation of Type VI , Part I, Publications of the Research Institute for Mathematical Sciences, vol.42, issue.4
DOI : 10.2977/prims/1166642194

J. Jost and S. Yau, The strong rigidity of locally symmetric complex manifolds of rank one and finite volume, Mathematische Annalen, vol.100, issue.2, pp.291-304, 1986.
DOI : 10.1007/BF01458463

J. Jost and K. Zuo, Harmonic maps and SL(r, C) representations of fundamental groups of quasiprojective manifolds, J. Algebraic Geom, vol.5, pp.77-106, 1996.

J. Jost and K. Zuo, Harmonic maps into Bruhat-Tits buildings and factorizations of p-adically unbounded representations of ? 1 of algebraic varieties I, J. Alg. Geom, vol.9, pp.1-42, 2000.

M. Kapovich and J. Millson, On representation varieties of Artin groups, projective arrangements and the fundamental groups of smooth complex algebraic varieties, Publications math??matiques de l'IH??S, vol.14, issue.1, pp.5-95, 1998.
DOI : 10.1007/BF02701766

N. Katz, Exponential Sums and Differential Equations, Annals of Mathematics Studies, vol.124, 1990.

N. Katz, Rigid local systems, Annals of Mathematics Studies, vol.139, 1996.
DOI : 10.1515/9781400882595

L. Katzarkov, On the Shafarevich maps Algebraic geometry?Santa Cruz, Proc. Sympos. Pure Math. 62, Part, pp.173-216, 1995.

L. Katzarkov and M. Ramachandran, On the universal coverings of algebraic surfaces, Annales Scientifiques de l?????cole Normale Sup??rieure, vol.31, issue.4, pp.31525-535, 1998.
DOI : 10.1016/S0012-9593(98)80105-5

T. Kawasaki, The signature theorem for V-manifolds, Topology, vol.17, issue.1, pp.75-83, 1978.
DOI : 10.1016/0040-9383(78)90013-7

S. Keel and S. Mori, Quotients by Groupoids, The Annals of Mathematics, vol.145, issue.1, pp.193-213, 1997.
DOI : 10.2307/2951828

B. Klingler, Sur la rigidité de certains groupes fondamentaux, l'arithméticité des réseaux hyperboliques complexes, et les " faux plans projectifs, pp.105-143, 2003.

S. Kobayashi and T. Ochiai, Meromorphic mappings onto compact complex spaces of general type, Inventiones Mathematicae, vol.212, issue.1, pp.7-16, 1975.
DOI : 10.1007/BF01389863

J. Kollar, Shafarevich maps and plurigenera of algebraic varieties, Inventiones Mathematicae, vol.16, issue.1, pp.177-215, 1993.
DOI : 10.1007/BF01244307

H. Konno, Construction of the moduli space of stable parabolic Higgs bundles on a Riemann surface, Journal of the Mathematical Society of Japan, vol.45, issue.2, pp.253-276, 1993.
DOI : 10.2969/jmsj/04520253

M. Kontsevich, Notes on Motives in Finite Characteristic
DOI : 10.1007/978-0-8176-4747-6_7

R. Kottwitz, Points on some Shimura varieties over finite fields, Journal of the American Mathematical Society, vol.5, issue.2, pp.373-444, 1992.
DOI : 10.1090/S0894-0347-1992-1124982-1

S. Lang, Diophantine geometry. Interscience Tracts in Pure and Applied Mathematics 11 Interscience Publishers, 1962.

Y. Laszlo and M. Olsson, The six operations for sheaves on Artin stacks II: Adic coefficients, Publications math??matiques de l'IH??S, vol.65, issue.1
DOI : 10.1007/s10240-008-0012-5
URL : https://hal.archives-ouvertes.fr/hal-00022034

M. Larsen and R. Pink, On ? of algebraic monodromy groups in compatible systems of representations, Inventiones Mathematicae, vol.247, issue.No. 4, pp.603-636, 1992.
DOI : 10.1007/BF01231904

M. Larsen, Arithmetic compactification of some Shimura surfaces. The zeta functions of Picard modular surfaces, Univ. Montréal, pp.31-45, 1992.

G. Laumon and L. Moret-bailly, Champs algébriques, Ergebnisse der Mathematik und ihrer Grenzgebiete 39, 2000.

J. Li, Hermitian-Einstein metrics and Chern number inequalities on parabolic stable bundles over Kähler manifolds, Comm. Anal. Geom, vol.8, pp.445-475, 2000.

J. Li and M. S. Narasimhan, Hermitian-einstein metrics on parabolic stable bundles, Acta Mathematica Sinica, English Series, vol.17, issue.1, pp.93-114, 1999.
DOI : 10.1007/s10114-999-0062-8

J. Li and M. S. Narasimhan, A Note on Hermitian-Einstein Metrics on Parabolic Stable Bundles, Acta Mathematica Sinica, English Series, vol.88, issue.1, pp.77-80, 2001.
DOI : 10.1007/s101140000091

A. Lubotsky and A. Magid, Varieties of representations of finitely generated groups, Memoirs of the American Mathematical Society, vol.58, issue.336, p.58, 1985.
DOI : 10.1090/memo/0336

C. Mcmullen, Billiards and Teichmüller curves on Hilbert modular surfaces, Journal of the American Mathematical Society, vol.16, issue.04, pp.857-885, 2003.
DOI : 10.1090/S0894-0347-03-00432-6

T. Mochizuki, Asymptotic Behaviour of Tame Nilpotent Harmonic Bundles with Trivial Parabolic Structure, Journal of Differential Geometry, vol.62, issue.3, pp.351-559, 2002.
DOI : 10.4310/jdg/1090426286