The authors establish positive and negative rationality results for certain real threefolds that are conic or quadric surface bundles with connected real locus and vanishing intermediate Jacobian obstruction.
Knebusch, On algebraic curves over real closed fields
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On the rationality of some real threefolds
The authors establish positive and negative rationality results for certain real threefolds that are conic or quadric surface bundles with connected real locus and vanishing intermediate Jacobian obstruction.