On representation varieties of Artin groups, projective arrangements and the fundamental groups of smooth complex algebraic varieties

 Access to full text

 Full (PDF)

1. [AK] S. AKBULUT, H. KING, Topology of Real Algebraic Sets, MSRI Publications, 25 (1992), Springer-Verlag. Zbl0808.14045MR94m:57001
2. [ABC] J. AMOROS, M. BURGER, K. CORLETTE, D. KOTSCHICK, D. TOLEDO, Fundamental groups of Kähler manifolds, AMS Mathematical Surveys and Monographs, 44, 1996. Zbl0849.32006MR97d:32037
3. [AN] D. ARAPURA, M. NORI, Solvable fundamental groups of algebraic varieties and Kähler manifolds, Preprint, June 1997. Zbl0971.14020
4. [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. MR83d:58016
5. [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. MR83d:58016
6. [Ar] M. ARTIN, On the solutions of analytic equations, Invent. Math., 5 (1968), 277-291. Zbl0172.05301MR38 #344
7. [AM] M. ATIYAH, I. MACDONALD, Introduction to Commutative Algebra, Addison-Wesley, 1969. Zbl0175.03601MR39 #4129
8. [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. Zbl0896.14006
9. [Bo] N. BOURBAKI, Groupes et algèbres de Lie, Chap. 4 à 6, Masson, 1981. Zbl0483.22001
10. [BuM] R. O. BUCHWEITZ, J. J. MILLSON, CR-geometry and deformations of isolated singularities, Memoirs of AMS, 125, N 597 (1997). Zbl0871.32023MR97g:32045
11. [B] E. BRIESKORN, Die Fundamentalgruppe des Raumes der regulären Orbits einer endlichen komplexen Spiegelungsgruppe, Inventiones Math., 12 (1971), 57-61. Zbl0204.56502MR45 #2692
12. [BS] E. BRIESKORN, K. SAITO, Artin-Gruppen und Coxeter-Gruppen, Inventiones Math., 17 (1972), 245-271. Zbl0243.20037MR48 #2263
13. [C] H. S. M. COXETER, Finite unitary groups generated by reflections, Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 31 (1967), 125-135. Zbl0189.32302MR37 #6358
14. [D1] P. DELIGNE, Théorie de Hodge II, Publications Math. IHES, 40 (1971), 5-58. Zbl0219.14007MR58 #16653a
15. [D2] P. DELIGNE, Théorie de Hodge III, Publications Math. IHES, 44 (1974), 5-77. Zbl0237.14003MR58 #16653b
16. [DGMS] P. DELIGNE, P. GRIFFTTH, J. MORGAN, D. SULLIVAN, Real homotopy theory of Kähler manifolds, Inventiones Math., 29 (1975), 245-274. Zbl0312.55011
17. [DG] M. DEMAZURE, P. GABRIEL, Groupes algébriques: Vol. I. Géométrie algébrique, généralités, groupes commutatifs, Paris, Masson, 1970. Zbl0203.23401
18. [Di] A. DIMCA, Topics on Real and Complex Singularities, Advanced Lectures in Mathematics, Vieweg, 1987. Zbl0628.14001MR92d:32048
19. [EH] D. EISENBUD, J. HARRIS, Schemes: the language of the modern algebraic geometry, Wadsworth & Brooks/Cole Math. Series, 1992. Zbl0745.14002
20. [EN] D. EISENBUD, W. NEUMANN, Three-dimensional link theory and invariants of plane curve singularities, Ann. of Math. Stud., Princeton Univ. Press, 110 (1985). Zbl0628.57002MR87g:57007
21. [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. Zbl0678.53059MR90b:32041
22. [GrM] P. GRIFFITHS, J. MORGAN, Rational homotopy theory and differential forms, Progress in Mathematics, Birkhäuser, 1981. Zbl0474.55001MR82m:55014
23. [Hai] R. HAIN, in preparation. 
24. [H] R. HARTSHORNE, Foundations of Projective Geometry, Benjamin Inc., NY, 1967. Zbl0152.38702MR36 #5801
25. [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. Zbl0664.53023MR88j:22010
26. [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. Zbl0872.53035MR97i:58184
27. [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. Zbl0855.32013MR97h:57029
28. [KM3] M. KAPOVICH, J. J. MILLSON, Hodge theory and the art of paper folding, Publications of RIMS, Kyoto, 33 (1997), 1-33. Zbl0961.32026MR98a:58028
29. [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. Zbl0936.14010MR2000g:14019
30. [KM5] M. KAPOVICH, J. J. MILLSON, Universality theorems for configuration spaces of planar linkages, Preprint, 1998. Zbl1056.14077
31. [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. Zbl08.0544.04JFM08.0544.04
32. [Le] H. van der LEK, Extended Artin groups, Proc. of Symp. in Pure Math., 40 (1983), Part 2, p. 117-121. Zbl0523.14005MR85b:14005
33. [Lo] E. LOOIJENGA, Invariant theory for generalized root systems, Inventiones Math., 61 (1980), 1-32. Zbl0436.17005MR82f:17011
34. [LM] A. LUBOTZKY, A. MAGID, Varieties of representations for finitely generated groups, Memoirs of AMS, 336 (1985), N 5. Zbl0598.14042MR87c:20021
35. [Mi] J. J. MILLSON, Rational homotopy theory and deformation problems from algebraic geometry, Proc. of ICM 1990, I, p. 549-558. Zbl0761.32011MR93b:14008a
36. [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. Zbl0667.52006MR90a:52013
37. [Mo1] J. MORGAN, Hodge theory for the algebraic topology of smooth algebraic varieties, Proc. Symp. in Pure Math., 32 (1978), 119-127. Zbl0417.14005MR80g:32013
38. [Mo2] J. MORGAN, The algebraic topology of smooth algebraic varieties, Publications Math. IHES, 48 (1978), 137-204. Zbl0401.14003MR80e:55020
39. [N] P. E. NEWSTEAD, Introduction to Moduli Problems and Orbit Spaces, Tata Institute Lecture Notes, 1978. Zbl0411.14003MR81k:14002
40. [Sh] G. SHEPHARD, Regular complex polytopes, Proc. London Math. Soc., 2 (1952), 82-97. Zbl0047.14106MR13,968k
41. [Si] C. SIMPSON, Higgs bundles and local systems, Publications Math. IHES, 75 (1992), 5-95. Zbl0814.32003MR94d:32027
42. [St] K. G. C. von STAUDT, Beiträge zur Geometre der Lage, Heft 2, 1857. 
43. [Su1] D. SULLIVAN, Infinitesimal computations in topology, Publications Math. IHES, 47 (1977), 269-331. Zbl0374.57002MR58 #31119
44. [Sum] H. SUMIHIRO, Equivariant completion, J. Math. Kyoto Univ., 14 (1974), 1-28; 15 (1975), 573-605. Zbl0277.14008