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arXiv · 1402.4153

Hypersurfaces quartiques de dimension 3 : non rationalit\'e stable

Jean-Louis Colliot-Thélène·Alena Pirutka
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Abstract

Inspir\'es par un argument de C. Voisin, nous montrons l'existence d'hypersurfaces quartiques lisses dans ${\bf P}^4_{\mathbb C}$ qui ne sont pas stablement rationnelles, plus pr\'ecis\'ement dont le groupe de Chow de degr\'e z\'ero n'est pas universellement \'egal \`a $\mathbb Z$. --- There are (many) smooth quartic hypersurfaces in ${\bf P}^4_{\mathbb C}$ 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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Jean-Louis Colliot-Thélène, Alena Pirutka. 2014-02-17. Hypersurfaces quartiques de dimension 3 : non rationalit\'e stable. https://arxiv.org/abs/1402.4153

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