Geodesic
Families of algebraic curves with fixed degeneracies
Izvestiya. Mathematics , Tome 5 (1971) no. 6, pp. 1277-1302

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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. 
@article{IM2_1971_5_6_a5,
     author = {S. Yu. Arakelov},
     title = {Families of algebraic curves with fixed degeneracies},
     journal = {Izvestiya. Mathematics },
     pages = {1277--1302},
     publisher = {mathdoc},
     volume = {5},
     number = {6},
     year = {1971},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1971_5_6_a5/}
}
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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/