Hypersurfaces quartiques de dimension 3 : non rationalité stable

2014/02/17 by Colliot-Thélène, Jean-Louis, Pirutka, Alena · 5 citations
#14C15 #14D06 #14E08 #14F22 #14M20 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1402.4153

Abstract

Inspirés par un argument de C. Voisin, nous montrons l'existence d'hypersurfaces quartiques lisses dans \bf P⁴_{\mathbb C} qui ne sont pas stablement rationnelles, plus précisément dont le groupe de Chow de degré zéro n'est pas universellement égal à \mathbb Z. --- There are (many) smooth quartic hypersurfaces in \bf P⁴_{\mathbb C} which are not stably rational. More precisely, their degree zero Chow group is not universally equal to \mathbb Z. The proof uses a variation of a specialisation method due to C. Voisin.

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• Unboundedness of zero-cycles on higher dimensional Fano manifolds
• Torsion order and irrationality of complete intersections
• Nonrational varieties with unirational parametrizations of coprime degrees
• Specialization and rigidity
• Variétés réelles connexes non stablement rationnelles

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