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arxiv: 1104.1861 · v4 · submitted 2011-04-11 · 🧮 math.AG · math.AC

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Sur le produit de vari\'et\'es localement factorielles ou Q-factorielles

Samuel Boissi\`ere , Ofer Gabber , Olivier Serman
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classification 🧮 math.AG math.AC
keywords factorialfieldvarietiesalgebraiclocallyq-factorialalgebraicallyclosed
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We show that the factorial and Q-factorial loci of algebraic varieties defined over an algebraically closed field are open, that products of locally factorial varieties are still locally factorial, and that this property remains true for Q-factorial varieties if the ground field is not the algebraic closure of a finite field.

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