Three-dimensional quartic threefolds: stable non-rationality

DOI10.24033/ASENS.2285zbMATH Open1371.14028arXiv1402.4153OpenAlexW2964170647MaRDI QIDQ2811182

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Publication date: 10 June 2016

Published in: (Search for Journal in Brave)

Abstract: Inspir'es par un argument de C. Voisin, nous montrons l'existence d'hypersurfaces quartiques lisses dans $$ qui ne sont pas stablement rationnelles, plus pr'ecis'ement dont le groupe de Chow de degr'e z'ero n'est pas universellement 'egal `a $mathbbZ$. --- There are (many) smooth quartic hypersurfaces in $$ which are not stably rational. More precisely, their degree zero Chow group is not universally equal to $mathbbZ$. The proof uses a variation of a specialisation method due to C. Voisin.

Full work available at URL: https://arxiv.org/abs/1402.4153

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