About: De Franchis theorem

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In mathematics, the de Franchis theorem is one of a number of closely related statements applying to compact Riemann surfaces, or, more generally, algebraic curves, X and Y, in the case of genus g > 1. The simplest is that the automorphism group of X is finite (see though Hurwitz's automorphisms theorem). More generally, * the set of non-constant morphisms from X to Y is finite; * fixing X, for all but a finite number of such Y, there is no non-constant morphism from X to Y.

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rdfs:label	De Franchis theorem (en) Théorème de De Franchis (fr)
rdfs:comment	In mathematics, the de Franchis theorem is one of a number of closely related statements applying to compact Riemann surfaces, or, more generally, algebraic curves, X and Y, in the case of genus g > 1. The simplest is that the automorphism group of X is finite (see though Hurwitz's automorphisms theorem). More generally, * the set of non-constant morphisms from X to Y is finite; * fixing X, for all but a finite number of such Y, there is no non-constant morphism from X to Y. (en) En mathématiques, le théorème de Franchis est u ensemble d'énoncés sur les surfaces de Riemann compactes, et, plus généralement, aux courbes algébriques, X et Y, dans le cas du genre g > 1. La plus simple est que le groupe d'automorphismes de X est fini (voir cependant le théorème des automorphismes de Hurwitz). Plus généralement, * l'ensemble des morphismes non constants de X vers Y est fini ; * soit X fixé, pour tous sauf un nombre fini de tels Y, il n'y a pas de morphisme non constant de X vers Y. (fr)
dcterms:subject	Riemann surfaces Theorems in algebraic topology Theorems in algebraic geometry Algebraic curves
Wikipage page ID	3094697 (xsd:integer)
Wikipage revision ID	969622371 (xsd:integer)
Link from a Wikipage to another Wikipage	Mordell conjecture Riemann surfaces Mathematics Genus (mathematics) Gerd Faltings Morphism Automorphism Theorems in algebraic topology Algebraic curve Francesco Severi Hurwitz's automorphisms theorem Theorems in algebraic geometry Algebraic curves Castelnuovo–de Franchis theorem Compact Riemann surface
sameAs	De Franchis theorem De Franchis theorem De Franchis theorem De Franchis theorem De Franchis theorem
dbp:wikiPageUsesTemplate	dbt:Ill dbt:Short_description dbt:Algebraic_curves_navbox
has abstract	In mathematics, the de Franchis theorem is one of a number of closely related statements applying to compact Riemann surfaces, or, more generally, algebraic curves, X and Y, in the case of genus g > 1. The simplest is that the automorphism group of X is finite (see though Hurwitz's automorphisms theorem). More generally, * the set of non-constant morphisms from X to Y is finite; * fixing X, for all but a finite number of such Y, there is no non-constant morphism from X to Y. These results are named for Michele De Franchis (1875–1946). It is sometimes referenced as the De Franchis-Severi theorem. It was used in an important way by Gerd Faltings to prove the Mordell conjecture. (en) En mathématiques, le théorème de Franchis est u ensemble d'énoncés sur les surfaces de Riemann compactes, et, plus généralement, aux courbes algébriques, X et Y, dans le cas du genre g > 1. La plus simple est que le groupe d'automorphismes de X est fini (voir cependant le théorème des automorphismes de Hurwitz). Plus généralement, * l'ensemble des morphismes non constants de X vers Y est fini ; * soit X fixé, pour tous sauf un nombre fini de tels Y, il n'y a pas de morphisme non constant de X vers Y. Ces résultats portent le nom de Michele de Franchis (1875-1946). Gerd Faltings en a fait un usage crucial pour démontrer la conjecture de Mordell. (fr)
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prov:wasDerivedFrom	wikipedia-en:De_Franchis_theorem?oldid=969622371&ns=0
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foaf:isPrimaryTopicOf	wikipedia-en:De_Franchis_theorem
is Link from a Wikipage to another Wikipage of	De franchis theorem Michele de Franchis Castelnuovo–de Franchis theorem List of theorems
is Wikipage redirect of	De franchis theorem
is foaf:primaryTopic of	wikipedia-en:De_Franchis_theorem

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