On representation varieties of Artin groups, projective arrangements and the fundamental groups of smooth complex algebraic varieties
Publications Mathématiques de l'IHÉS, Tome 88 (1998), pp. 5-95 
@article{PMIHES_1998__88__5_0,
     author = {Kapovich, Michael and Millson, John J.},
     title = {On representation varieties of {Artin} groups, projective arrangements and the fundamental groups of smooth complex algebraic varieties},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {5--95},
     year = {1998},
     publisher = {Institut des Hautes Etudes Scientifiques},
     volume = {88},
     mrnumber = {1733326},
     zbl = {0982.20023},
     language = {en},
     url = {https://www.numdam.org/item/PMIHES_1998__88__5_0/}
}
TY  - JOUR
AU  - Kapovich, Michael
AU  - Millson, John J.
TI  - On representation varieties of Artin groups, projective arrangements and the fundamental groups of smooth complex algebraic varieties
JO  - Publications Mathématiques de l'IHÉS
PY  - 1998
SP  - 5
EP  - 95
VL  - 88
PB  - Institut des Hautes Etudes Scientifiques
UR  - https://www.numdam.org/item/PMIHES_1998__88__5_0/
LA  - en
ID  - PMIHES_1998__88__5_0
ER  - 
%0 Journal Article
%A Kapovich, Michael
%A Millson, John J.
%T On representation varieties of Artin groups, projective arrangements and the fundamental groups of smooth complex algebraic varieties
%J Publications Mathématiques de l'IHÉS
%D 1998
%P 5-95
%V 88
%I Institut des Hautes Etudes Scientifiques
%U https://www.numdam.org/item/PMIHES_1998__88__5_0/
%G en
%F PMIHES_1998__88__5_0
Kapovich, Michael; Millson, John J. On representation varieties of Artin groups, projective arrangements and the fundamental groups of smooth complex algebraic varieties. Publications Mathématiques de l'IHÉS, Tome 88 (1998), pp. 5-95. https://www.numdam.org/item/PMIHES_1998__88__5_0/

[AK] S. Akbulut, H. King, Topology of Real Algebraic Sets, MSRI Publications, 25 (1992), Springer-Verlag. | Zbl | MR

[ABC] J. Amoros, M. Burger, K. Corlette, D. Kotschick, D. Toledo, Fundamental groups of Kähler manifolds, AMS Mathematical Surveys and Monographs, 44, 1996. | Zbl | MR

[AN] D. Arapura, M. Nori, Solvable fundamental groups of algebraic varieties and Kähler manifolds, Preprint, June 1997. | Zbl

[A1] V. I. Arnold, Normal forms of functions in neighborhoods of degenerate critical points, In: Lecture Notes of London Math. Soc., 53 (1981), Singularity Theory, 91-131. | MR

[A2] V. I. Arnold, Critical points of smooth functions and their normal forms, In: Lecture Notes of London Math. Soc., 53 (1981), Singularity Theory, 132-206. | MR

[Ar] M. Artin, On the solutions of analytic equations, Invent. Math., 5 (1968), 277-291. | Zbl | MR

[AM] M. Atiyah, I. Macdonald, Introduction to Commutative Algebra, Addison-Wesley, 1969. | Zbl | MR

[BiM] E. Bierstone, P. Millman, Canonical desingularization in characteristic zero by blowing up maximal strata of a local invariant, Inventiones Math., 128 (1997), 207-320. | Zbl

[Bo] N. Bourbaki, Groupes et algèbres de Lie, Chap. 4 à 6, Masson, 1981. | Zbl

[BuM] R. O. Buchweitz, J. J. Millson, CR-geometry and deformations of isolated singularities, Memoirs of AMS, 125, N 597 (1997). | Zbl | MR

[B] E. Brieskorn, Die Fundamentalgruppe des Raumes der regulären Orbits einer endlichen komplexen Spiegelungsgruppe, Inventiones Math., 12 (1971), 57-61. | Zbl | MR

[BS] E. Brieskorn, K. Saito, Artin-Gruppen und Coxeter-Gruppen, Inventiones Math., 17 (1972), 245-271. | Zbl | MR

[C] H. S. M. Coxeter, Finite unitary groups generated by reflections, Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 31 (1967), 125-135. | Zbl | MR

[D1] P. Deligne, Théorie de Hodge II, Publications Math. IHES, 40 (1971), 5-58. | Zbl | MR | Numdam

[D2] P. Deligne, Théorie de Hodge III, Publications Math. IHES, 44 (1974), 5-77. | Zbl | MR | Numdam

[DGMS] P. Deligne, P. Grifftth, J. Morgan, D. Sullivan, Real homotopy theory of Kähler manifolds, Inventiones Math., 29 (1975), 245-274. | Zbl

[DG] M. Demazure, P. Gabriel, Groupes algébriques: Vol. I. Géométrie algébrique, généralités, groupes commutatifs, Paris, Masson, 1970. | Zbl

[Di] A. Dimca, Topics on Real and Complex Singularities, Advanced Lectures in Mathematics, Vieweg, 1987. | Zbl | MR

[EH] D. Eisenbud, J. Harris, Schemes: the language of the modern algebraic geometry, Wadsworth & Brooks/Cole Math. Series, 1992. | Zbl

[EN] D. Eisenbud, W. Neumann, Three-dimensional link theory and invariants of plane curve singularities, Ann. of Math. Stud., Princeton Univ. Press, 110 (1985). | Zbl | MR

[GM] W. Goldman, J. J. Millson, The deformation theory of representations of fundamental groups of compact Kähler manifolds, Publications Math. IHES, 67 (1988), 43-96. | Zbl | MR | Numdam

[GrM] P. Griffiths, J. Morgan, Rational homotopy theory and differential forms, Progress in Mathematics, Birkhäuser, 1981. | Zbl | MR

[Hai] R. Hain, in preparation.

[H] R. Hartshorne, Foundations of Projective Geometry, Benjamin Inc., NY, 1967. | Zbl | MR

[JM] D. Jonhson, J. J. Millson, Deformation spaces associated to compact hyperbolic manifolds, In: Discrete Groups in Geometry and Analysis, Papers in honor of G. D. Mostow on his 60-th birthday, R. Howe (ed.), Progress in Mathematics, 67 (1987), Birkhäuser, 48-106. | Zbl | MR

[KM1] M. Kapovich, J. J. Millson, The relative deformation theory of representations and flat connections and deformations of linkages in constant curvature spaces, Compositio Math., 103 (1996), 287-317. | Zbl | MR | Numdam

[KM2] M. Kapovich, J. J. Millson, On the deformation theory of representations of fundamental groups of closed hyperbolic 3-manifolds, Topology, 35 (1996), 1085-1106. | Zbl | MR

[KM3] M. Kapovich, J. J. Millson, Hodge theory and the art of paper folding, Publications of RIMS, Kyoto, 33 (1997), 1-33. | Zbl | MR

[KM4] M. Kapovich, J. J. Millson, Moduli Spaces of Linkages and Arrangements, In: Advances in Geometry, J.-L. Brylinski (ed.), Progress in Mathematics, 172 (1999), Birkhäuser, 237-270. | Zbl | MR

[KM5] M. Kapovich, J. J. Millson, Universality theorems for configuration spaces of planar linkages, Preprint, 1998.

[Ke] A. B. Kempe, On a general method of describing plane curves of the n-th degree by linkwork, Proc. London Math. Soc., 7 (1875), 213-216. | JFM

[Le] H. Van Der Lek, Extended Artin groups, Proc. of Symp. in Pure Math., 40 (1983), Part 2, p. 117-121. | Zbl | MR

[Lo] E. Looijenga, Invariant theory for generalized root systems, Inventiones Math., 61 (1980), 1-32. | Zbl | MR

[LM] A. Lubotzky, A. Magid, Varieties of representations for finitely generated groups, Memoirs of AMS, 336 (1985), N 5. | Zbl | MR

[Mi] J. J. Millson, Rational homotopy theory and deformation problems from algebraic geometry, Proc. of ICM 1990, I, p. 549-558. | Zbl | MR

[Mn] N. Mnëv, The universality theorems on the classification problem of configuration varieties and convex polytopes varieties, Lecture Notes in Math., 1346 (1988), 527-543. | Zbl | MR

[Mo1] J. Morgan, Hodge theory for the algebraic topology of smooth algebraic varieties, Proc. Symp. in Pure Math., 32 (1978), 119-127. | Zbl | MR

[Mo2] J. Morgan, The algebraic topology of smooth algebraic varieties, Publications Math. IHES, 48 (1978), 137-204. | Zbl | MR | Numdam

[N] P. E. Newstead, Introduction to Moduli Problems and Orbit Spaces, Tata Institute Lecture Notes, 1978. | Zbl | MR

[Sh] G. Shephard, Regular complex polytopes, Proc. London Math. Soc., 2 (1952), 82-97. | Zbl | MR

[Si] C. Simpson, Higgs bundles and local systems, Publications Math. IHES, 75 (1992), 5-95. | Zbl | MR | Numdam

[St] K. G. C. Von Staudt, Beiträge zur Geometre der Lage, Heft 2, 1857.

[Su1] D. Sullivan, Infinitesimal computations in topology, Publications Math. IHES, 47 (1977), 269-331. | Zbl | MR | Numdam

[Sum] H. Sumihiro, Equivariant completion, J. Math. Kyoto Univ., 14 (1974), 1-28; 15 (1975), 573-605. | Zbl