A simple remark on fields of definition
Let K< L be an extension of fields, in characteristic zero, with L algebraically closed and let ¯K < L be the algebraic closure of K in L. Let X and Y be irreducible projective algebraic varieties, X defined over ¯K and Y defined over L, and let π : X →Y be a non-constant mo...
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Universidad Católica del Norte, Departamento de Matemáticas
2012
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oai:scielo:S0716-091720120001000032012-04-13A simple remark on fields of definitionHidalgo,Rubén Algebraic curves field of moduli field of definition Let K< L be an extension of fields, in characteristic zero, with L algebraically closed and let ¯K < L be the algebraic closure of K in L. Let X and Y be irreducible projective algebraic varieties, X defined over ¯K and Y defined over L, and let π : X →Y be a non-constant morphism, defined over L. If we assume that ¯K ≠ L, then one may wonder if Y is definable over ¯K. In the case that K = Q, L = C and that X and Y are smooth curves, a positive answer was obtained by Gonzalez-Diez. In this short note we provide simple conditions to have a positive answer to the above question. We also state a conjecture for a class of varieties of general type.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.31 n.1 20122012-03-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172012000100003en10.4067/S0716-09172012000100003 |
| institution |
Scielo Chile |
| collection |
Scielo Chile |
| language |
English |
| topic |
Algebraic curves field of moduli field of definition |
| spellingShingle |
Algebraic curves field of moduli field of definition Hidalgo,Rubén A simple remark on fields of definition |
| description |
Let K< L be an extension of fields, in characteristic zero, with L algebraically closed and let ¯K < L be the algebraic closure of K in L. Let X and Y be irreducible projective algebraic varieties, X defined over ¯K and Y defined over L, and let π : X →Y be a non-constant morphism, defined over L. If we assume that ¯K ≠ L, then one may wonder if Y is definable over ¯K. In the case that K = Q, L = C and that X and Y are smooth curves, a positive answer was obtained by Gonzalez-Diez. In this short note we provide simple conditions to have a positive answer to the above question. We also state a conjecture for a class of varieties of general type. |
| author |
Hidalgo,Rubén |
| author_facet |
Hidalgo,Rubén |
| author_sort |
Hidalgo,Rubén |
| title |
A simple remark on fields of definition |
| title_short |
A simple remark on fields of definition |
| title_full |
A simple remark on fields of definition |
| title_fullStr |
A simple remark on fields of definition |
| title_full_unstemmed |
A simple remark on fields of definition |
| title_sort |
simple remark on fields of definition |
| publisher |
Universidad Católica del Norte, Departamento de Matemáticas |
| publishDate |
2012 |
| url |
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172012000100003 |
| work_keys_str_mv |
AT hidalgoruben asimpleremarkonfieldsofdefinition AT hidalgoruben simpleremarkonfieldsofdefinition |
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