Non-rationality of the symmetric sextic Fano threefold

  • Arnaud Beauville

    Université de Nice, France
Non-rationality of the symmetric sextic Fano threefold cover
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Abstract

We prove that the symmetric sextic Fano threefold, defined by the equations in , is not rational. In view of the work of Prokhorov [P], our result implies that the alternating group admits only one embedding into the Cremona group up to conjugacy.