Plane curves with hyperbolic and C-hyperbolic complements
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 23 (1996) no. 4, pp. 749-778.
@article{ASNSP_1996_4_23_4_749_0,
     author = {Dethloff, G. and Zaidenberg, M.},
     title = {Plane curves with hyperbolic and $C$-hyperbolic complements},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {749--778},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 23},
     number = {4},
     year = {1996},
     mrnumber = {1469573},
     zbl = {0919.32015},
     language = {en},
     url = {http://archive.numdam.org/item/ASNSP_1996_4_23_4_749_0/}
}
TY  - JOUR
AU  - Dethloff, G.
AU  - Zaidenberg, M.
TI  - Plane curves with hyperbolic and $C$-hyperbolic complements
JO  - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY  - 1996
SP  - 749
EP  - 778
VL  - 23
IS  - 4
PB  - Scuola normale superiore
UR  - http://archive.numdam.org/item/ASNSP_1996_4_23_4_749_0/
LA  - en
ID  - ASNSP_1996_4_23_4_749_0
ER  - 
%0 Journal Article
%A Dethloff, G.
%A Zaidenberg, M.
%T Plane curves with hyperbolic and $C$-hyperbolic complements
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 1996
%P 749-778
%V 23
%N 4
%I Scuola normale superiore
%U http://archive.numdam.org/item/ASNSP_1996_4_23_4_749_0/
%G en
%F ASNSP_1996_4_23_4_749_0
Dethloff, G.; Zaidenberg, M. Plane curves with hyperbolic and $C$-hyperbolic complements. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 23 (1996) no. 4, pp. 749-778. http://archive.numdam.org/item/ASNSP_1996_4_23_4_749_0/

[1] P. Aluffi - C. Faber, Linear orbits of d-tuples of points in P1, J. Reine Angew. Math. 445 (1993), 205-220. | MR | Zbl

[2] A.B. Aure, Plücker conditions on plane rational curves, Math. Scand 55 (1984), 47-58, with Appendix by S.A. Strömme, ibid. 59-61. | MR | Zbl

[3] K. Azukawa - M. Suzuki, Some examples of algebraic degeneracy and hyperbolic manifolds, Rocky Mountain J. Math 10 (1980), 655-659. | MR | Zbl

[4] J.A. Carlson - M. Green, Holomorphic curves in the plane, Duke Math. J. 43 (1976), 1-9. | MR | Zbl

[5] A.I. Degtyarev, Topology of plane projective algebraic curves, PhD Thesis, Leningrad State University, 1987 (in Russian).

[6] A. Degtyarev, Quintics in CP2 with nonabelianfundamental group, preprint, Max-Planck-Institut für Mathematik, Bonn, 1995, 21p.

[7] P. Deligne, Le groupe fondamental du complement d'une courbe plane n'ayant que des points doubles ordinaries est abélien, Sem. Bourbaki, 1979/1980, Lecture Notes in Math. 842, Springer-Verlag, N.Y., 1981, 1-25. | Numdam | MR | Zbl

[8] G. Dethloff - G. Schumacher - P.-M. Wong, Hyperbolicity of the complements of plane algebraic curves, Amer. J. Math. 117 (1995), 573-599. | MR | Zbl

[9] G. Dethloff - G. Schumacher - P.-M. Wong, On the hyperbolicity of the complement of curves in algebraic surfaces: The three component case, Duke Math. J. 78 (1995), 193-212. | MR | Zbl

[10] G. Dethloff - M. Zaidenberg, Examples of plane curves of low degrees with hyperbolic and C-hyperbolic complements, Proc. Conf. "Geometric Complex Analysis", Hayama, March 19-29, 1995, J. Noguchi a.e. eds., World Scientific Singapore e.a., 1996, 147-161. | MR | Zbl

[11] I. Dolgachev - A. Libgober, On the fundamental group of the complement to a discriminant variety, in: Algebraic Geometry, Lecture Notes in Math. 862 Springer N.Y. 1981, 1-25. | MR | Zbl

[12] H. Flenner - M. Zaidenberg, On a class of rational cuspidal plane curves, Manuscripta Math. 89 (1996), 439-459. | MR | Zbl

[13] W. Fulton, On the fundamental group of the complement to a node curve, Ann. of Math. 11 (1980), 407-409. | MR | Zbl

[14] I.M. Gelfand - M.M. Kapranov - A.V. Zelevinsky, Discriminants, Resultants and Multidimensional Determinants, Bikhäuser, Boston, 1994. | MR | Zbl

[15] H. Grauert - U. Peternell, Hyperbolicity of the complements of plane curves, Manuscripta Math. 50 (1985), 429-441. | MR | Zbl

[16] M. Green, The complement of the dual of a plane curve and some new hyperbolic manifolds, in: Value Distribution Theory, Kujala and Vitter eds., Marcel Dekker, N.Y., 1974, 119-131. | MR | Zbl

[17] M. Green, Some examples and counterexamples in value distribution theory, Compositio Math. 30 (1975), 317-322. | Numdam | MR | Zbl

[18] D. Hilbert, Theory of Algebraic Invariants, Cambridge University Press, Cambridge, 1993. | MR | Zbl

[19] Sh.I. Kaliman, The holomorphic universal covers of space of polynomials without multiple roots, Selecta Mathem. form. Sovietica 12 (1993), 395-405. | MR | Zbl

[20] J. Kaneko, On the fundamental group of the complement to a maximal cuspidal plane curve, Mem. Fac. Sci. Kyushu Univ. Ser. A. 39 (1985), 133-146. | MR | Zbl

[21] Sh. Kobayashi, Hyperbolic Manifolds and Holomorphic Mappings, Marcel Dekker, N.Y., 1970. | MR | Zbl

[22] V.Ja. Lin , Liouville coverings of complex spaces, and amenable groups, Math.USSR-Sb. 60 (1988), 197-216. | MR | Zbl

[23] K. Masuda - J. Noguchi, A construction of hyperbolic hypersurfaces of Pn (C), Math. Ann. 304 (1996), 339-362. | MR | Zbl

[24] A. Nadel, Hyperbolic surface in P3, Duke Math. J. 58 (1989), 749-771. | MR | Zbl

[25] M. Namba, Geometry of projective algebraic curves, Marcell Dekker, N.Y., 1984. | MR | Zbl

[26] M. Oka, Symmetric plane curves with nodes and cusps, J. Math. Soc. Japan 44 (1992), 375-414. | MR | Zbl

[27] A.Yu. Ol'Shanskiy - A.L. Shmel'Kin, Infinite groups, in: Algebra IV, Encyclopaeadia of Math. Sci. 37 Springer Berlin, 1993, 3-95.

[28] R. Piene, Cuspidal projections of space curves, Math. Ann. 256 (1981), 95-119. | MR | Zbl

[29] V. Popov - E. Vinberg, Invariant theory, in: Algebraic Geometry IV, Parshin and Shafarevich, eds., 123-278, Springer Berlin, 1994. | MR | Zbl

[30] H. Royden, Automorphisms and isometries of Teichmüller space, in: Advantances in the Theory of Riemann Surface, 1969 Stony Brook Conf. Ann. of Math. St. 66, Princeton Univ. Press, 1971, Princeton, N.J., 369-383. | MR | Zbl

[31] F. Severi, Vorlesungen über algebraische Geometrie, Leipzig: Teubner, 1921. | JFM

[32] Y.-T. Siu - S.-K. Yeung, Hyperbolicity of the complement of a generic smooth curve of high degree in the complex projective plane, Invent. Math. 124 (1996), 573-618. | MR | Zbl

[33] G. Veronese, Behandlung der projectivischen Verhältnisse der Räume von verschiedenen Dimensionen durch das Princip des Projicirens und Schneidens, Math. Ann. 19 (1882), 193-234. | JFM

[34] R.J. Walker, Algebraic Curves, Princeton Math. Series 13 Princeton University Press, Princeton, N.J., 1950. | MR | Zbl

[35] M. Zaidenberg, On hyperbolic embedding of complements of divisors and the limiting behavior of the Kobayashi-Royden metric, Math. USSR-Sb. 55 (1986), 55-70. | MR | Zbl

[36] M. Zaidenberg, Stability of hyperbolic imbeddedness and construction of examples, Math. USSR-Sb. 63 (1989), 351-361. | MR | Zbl

[37] M. Zaidenberg, Hyperbolicity in projective spaces, Proc. Conf. on Hyperbolic and Diophantine Analysis, RIMS, Kyoto, Oct. 26-30, 1992, TIT, Tokyo, 1992, 136-156. | MR

[38] O. Zariski, Collected Papers. Vol III: Topology of curves and surfaces, and special topics in the theory of algebraic varieties, The MIT Press, Cambridge Mass., 1978. | MR | Zbl