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Title:
Rationality of real conic bundles with quartic discriminant curve
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Abstract:
Clemens–Griffiths introduced the classical intermediate Jacobian obstruction to rationality for complex threefolds in their proof of the irrationality of the cubic threefold. Recently, over non-closed fields, Hassett–Tschinkel (over R) and Benoist–Wittenberg (over k) refined this obstruction using torsors over the intermediate Jacobian. In this talk, we describe this obstruction in the setting of conic bundle threefolds. In particular, we study rationality over the real numbers for a specific class of these conic bundles. This talk is based on joint work with S. Frei–S. Sankar–B. Viray–I. Vogt and on joint work with M. Ji.
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