Harvard-MIT Algebraic Geometry Seminar: Obstructions to rationality for conic bundle threefolds


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May 10, 2022 3:00 pm - 4:00 pm
MIT Room 2-143

Bianca Viray - University of Washington

Benoist and Wittenberg recently introduced a new rationality obstruction that refines the classical the Clemens--Griffiths intermediate Jacobian obstruction to rationality, and exhibited its strength by showing that this new obstruction characterizes rationality for intersections of two quadrics.  We show that this phenomenon does not extend to all geometrically rational threefolds.  We construct examples of conic bundle threefolds over P^2 that have no refined intermediate Jacobian obstruction to rationality, yet fail to be rational. This is joint work with S. Frei, L. Ji, S. Sankar, and I. Vogt.