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One more counter-example to the Lüroth problem.
Arnaud Beauville (Université de Nice) The Lüroth problem asks whether every field K with C ⊂ K ⊂ C (x_1, . . . , x_n) is of the form C(y_1, . . . , y_p). In geometric terms, if an algebraic variety can be parametrized by rational functions, can one find a one-to-one such parametrization? After a brief historical survey, I will recall the counter-examples found in the 70's; then I will describe a quite simple (and new) counter-example. If time permits, I'll explain the relation with the study of the Cremona group in dimension 3. | ![]() |
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