Abstract:We study real double covers of P 1 ×P 2 branched over a (2, 2)-divisor, which have the structure of a conic bundle threefold with smooth quartic discriminant curve via the second projection. In each isotopy class of smooth plane quartics, we construct examples where the total space of the conic bundle is rational. For five of the six isotopy classes we construct C-rational examples that have obstructions to rationality over R, and for the sixth class, we show that the models we consider are all rational.Moreov… Show more
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