Geodesic
Dualizing coverings of the plane
Izvestiya. Mathematics , Tome 79 (2015) no. 5, pp. 1013-1042.

Voir la notice de l'article provenant de la source Math-Net.Ru

We study the properties of dualizing coverings of the plane which are associated with plane curves, and completely describe the set of curves for which all singularities of the Galoisation of the associated dualizing covering are quotient singularities.
Keywords: dual curves, coverings of the plane, quotient singularities, groups generated by reflections. 
@article{IM2_2015_79_5_a5,
     author = {Vik. S. Kulikov},
     title = {Dualizing coverings of the plane},
     journal = {Izvestiya. Mathematics },
     pages = {1013--1042},
     publisher = {mathdoc},
     volume = {79},
     number = {5},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2015_79_5_a5/}
}
TY  - JOUR
AU  - Vik. S. Kulikov
TI  - Dualizing coverings of the plane
JO  - Izvestiya. Mathematics 
PY  - 2015
SP  - 1013
EP  - 1042
VL  - 79
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2015_79_5_a5/
LA  - en
ID  - IM2_2015_79_5_a5
ER  - 
%0 Journal Article
%A Vik. S. Kulikov
%T Dualizing coverings of the plane
%J Izvestiya. Mathematics 
%D 2015
%P 1013-1042
%V 79
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2015_79_5_a5/
%G en
%F IM2_2015_79_5_a5
Vik. S. Kulikov. Dualizing coverings of the plane. Izvestiya. Mathematics , Tome 79 (2015) no. 5, pp. 1013-1042. http://geodesic.mathdoc.fr/item/IM2_2015_79_5_a5/

[1] K. Stein, “Analytische Zerlegungen komplexer Räume”, Math. Ann., 132 (1956), 63–93 | DOI | MR | Zbl

[2] F. Catanese, “On a problem of Chisini”, Duke Math. J., 53:1 (1986), 33–42 | DOI | MR | Zbl

[3] Vik. S. Kulikov, “On Chisini's conjecture”, Izv. Math., 63:6 (1999), 1139–1170 | DOI | DOI | MR | Zbl

[4] F. Bogomolov, Vik. S. Kulikov, “On the irreducibility of Hilbert scheme of surfaces of minimal degree”, Cent. Eur. J. Math., 11:2 (2013), 254–263 | DOI | MR | Zbl

[5] Vik. S. Kulikov, “Hurwitz curves”, Russian Math. Surveys, 62:6 (2007), 1043–1119 | DOI | DOI | MR | Zbl

[6] E. Ballico, A. Hefez, “On the Galois group associated to a generically étale morphism”, Comm. Algebra, 14:5 (1986), 899–909 | DOI | MR | Zbl

[7] H. Cartan, “Quotient d'un espace analytique par un groupe d'automorphismes”, Algebraic geometry and topology, A symposium in honor of S. Lefschetz (Princeton, 1954), Princeton Univ. Press, Princeton, NJ, 1957, 90–102 | MR | Zbl

[8] E. Brieskorn, “Rationale Singularitäten komplexer Flächen”, Invent. Math., 4:5 (1967/1968), 336–358 | DOI | MR | Zbl

[9] Yu. G. Prokhorov, Osobennosti algebraicheskikh mnogoobrazii, MTsNMO, M., 2009, 128 pp.

[10] G. C. Shephard, J. A. Todd, “Finite unitary reflection groups”, Canadian J. Math., 6 (1954), 274–304 | DOI | MR | Zbl

[11] F. Catanese, “Automorphisms of rational double points and moduli spaces of surfaces of general type”, Compositio Math., 61:1 (1987), 81–102 | MR | Zbl

[12] A. M. Cohen, “Finite complex reflection groups”, Ann. Sci. École Norm. Sup. (4), 9:3 (1976), 379–436 | MR | Zbl

[13] W. P. Barth, K. Hulek, C. A. M. Peters, A. Van de Ven, Compact complex surfaces, Ergeb. Math. Grenzgeb. (3), 4, 2nd ed., Springer-Verlag, Berlin, 2004, xii+436 pp. | DOI | MR | Zbl

[14] F. Klein, Vorlesungen über das Ikosaeder und die Auflösung der Gleichungen vom fünften Grade, Teubner, Leipzig, 1884, xxviii+343 pp. | MR | Zbl | Zbl