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Estimates of the number of rational mappings from a fixed variety to varieties of general type

Tanya BandmanGerd Dethloff — 1997

Annales de l'institut Fourier

First we find effective bounds for the number of dominant rational maps f : X Y between two fixed smooth projective varieties with ample canonical bundles. The bounds are of the type { A · K X n } { B · K X n } 2 , where n = dim X , K X is the canonical bundle of X and A , B are some constants, depending only on n . Then we show that for any variety X there exist numbers c ( X ) and C ( X ) with the following properties: For any threefold Y of general type the number of dominant rational maps f : X Y is bounded above by c ( X ) . The...

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