The main result of this paper is as follows: let be smooth projective threefolds (over a field of characteristic zero) such that . If is not a projective space, then the degree of a morphism is bounded in terms of discrete invariants of and . Moreover, suppose that and are smooth projective -dimensional with cyclic Néron-Severi groups. If , then the degree of is bounded iff is not a flat variety. In particular, to prove our main theorem we show the non-existence of a flat 3-dimensional projective variety with .
Le résultat principal de cet article est le théorème suivant : soient des variétés lisses projectives complexes de dimension trois telles que . Si n’est pas l’espace projectif, alors le degré d’un morphisme est borné (par des invariants discrets de et de ). En plus, supposons lisses projectives de dimension quelconque et telles que leurs groupes de Néron-Severi soient cycliques. Si , nous montrons que le degré de est borné si et seulement si n’est pas une variété plate. Une partie de la preuve du théorème principal revient donc à montrer la non-existence d’une variété projective plate de dimension trois avec .
@article{AIF_1999__49_2_405_0, author = {Amerik, Ekatarina and Rovinsky, Marat and Van De Ven, Antonius}, title = {A boundedness theorem for morphisms between threefolds}, journal = {Annales de l'Institut Fourier}, pages = {405--415}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {49}, number = {2}, year = {1999}, doi = {10.5802/aif.1679}, zbl = {0923.14008}, mrnumber = {2000f:14056}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1679/} }
TY - JOUR AU - Amerik, Ekatarina AU - Rovinsky, Marat AU - Van De Ven, Antonius TI - A boundedness theorem for morphisms between threefolds JO - Annales de l'Institut Fourier PY - 1999 SP - 405 EP - 415 VL - 49 IS - 2 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1679/ DO - 10.5802/aif.1679 LA - en ID - AIF_1999__49_2_405_0 ER -
%0 Journal Article %A Amerik, Ekatarina %A Rovinsky, Marat %A Van De Ven, Antonius %T A boundedness theorem for morphisms between threefolds %J Annales de l'Institut Fourier %D 1999 %P 405-415 %V 49 %N 2 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.1679/ %R 10.5802/aif.1679 %G en %F AIF_1999__49_2_405_0
Amerik, Ekatarina; Rovinsky, Marat; Van De Ven, Antonius. A boundedness theorem for morphisms between threefolds. Annales de l'Institut Fourier, Volume 49 (1999) no. 2, pp. 405-415. doi : 10.5802/aif.1679. https://aif.centre-mersenne.org/articles/10.5802/aif.1679/
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