Geodesic
Families of algebraic curves with fixed degeneracies
Izvestiya. Mathematics, Tome 5 (1971) no. 6, pp. 1277-1302 
S. Yu. Arakelov. Families of algebraic curves with fixed degeneracies. Izvestiya. Mathematics, Tome 5 (1971) no. 6, pp. 1277-1302. http://geodesic.mathdoc.fr/item/IM2_1971_5_6_a5/
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     author = {S. Yu. Arakelov},
     title = {Families of algebraic curves with fixed degeneracies},
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     number = {6},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1971_5_6_a5/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we prove that there exist only finitely many nonisomorphic and nonconstant curves of fixed genus, defined over a fixed function field and having bad reductions at a given finite set of points of this field.

[1] Parshin A. N., “Algebraicheskie krivye nad funktsionalnymi polyami”, Izv. AN SSSR. Ser. matem., 32 (1968), 1191–1219 | Zbl

[2] Mumford D., Geometric ivariant theory, Springer, Berlin, 1965 | MR | Zbl

[3] Mumford D., “Pathologies. III”, Amer. J. Math., 89:1 (1967), 94–104 | DOI | MR | Zbl

[4] Deligne P., Mumford D., “The irreducibility of the space of curves of given genus”, Publ. Math. Paris, 36 (1969), 75–109 | MR | Zbl

[5] Igusa J., “On the graded ring of theta-constants”, Amer. J. Math., 86:1 (1964), 219–243 | DOI | MR

[6] Weil A., “Zum Beweis des Torellischen Satzes”, Nachr. Akad. Wiss. Göttingen. Math.-Phys. Kl. IIa, 1957 (1957), 33–53 | MR

[7] Algebraicheskie poverkhnosti, Tr. Matem. in-ta im. V. A. Steklova AN SSSR, 75, 1965 | MR | Zbl

[8] Grotendik A., O nekotorykh voprosakh gomologicheskoi algebry, IL, M., 1961

[9] Artin M., Winters G., “Degenerate fibres and stable reduction for curves”, Topology, 1971 | MR

[10] Shafarevich I. R., “Polya algebraicheskikh chisel”, Proc. Intern. Congress Math. (Stockholm), 1962, 163–176