Rationality of singular cubic threefolds over $\mathbb R$

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arxiv 2411.14379 v1 pith:E3DY3AL4 submitted 2024-11-21 math.AG

Ivan Cheltsov , Yuri Tschinkel , Zhijia Zhang This is my paper · ORCID

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keywords cubicrationalitysingularthreefoldsmathbbpropertiesreal

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We study rationality properties of real singular cubic threefolds.

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Vari\'et\'es r\'eelles connexes non stablement rationnelles
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The first smooth intersections of two quadrics in P^5 and cubic threefolds in P^4 over the real Puiseux series field are semi-algebraically connected but not stably rational.
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For smooth geometrically rational real Fano threefolds with nonempty real locus, the absence of any deformation-equivalent real form with disconnected real locus forces R-rationality.