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- W2329060118 abstract "Introduction. In this paper we deal with the higher dimensional version of de Franchis' theorem which says that there are only a finite number of nonconstant separable rational mappings of an algebraic curve into a complete algebraic curve with genus greater than 1. KobayashiOchiai [11] proved that there are only a finite number of dominant meromorphic mappings onto a complex space of general type, and its algebraic proof which covers the positive characteristic case was given by [14] (cf. also [23]). Here we shall consider the case where the mappings are not necessarily dominant. Let k be an algebraically closed field with arbitrary characteristic. All algebraic varieties and mappings (morphisms) in the following will be defined over k. Let R be an algebraic variety, V a smooth complete algebraic variety, and T(V) denote the tangent bundle over V. Set rank f = sup {dim R - dimtf-1(f (t)); t E R } for rational mappings" @default.
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- W2329060118 date "1982-08-01" @default.
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- W2329060118 title "Finiteness of the Family of Rational and Meromorphic Mappings Into Algebraic Varieties" @default.
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- W2329060118 doi "https://doi.org/10.2307/2374210" @default.
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