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Rationality in families

Brendan Hassett (Brown)

Location:  Hill 705
Date & time: Friday, 13 April 2018 at 4:00PM - 5:00PM

Abstract: A complex variety is rational if it can be obtained from projective space by modifications, i.e., algebraic surgeries like blow-ups. Is rationality a deformation invariant for smooth projective varieties? This is the case for curves and surfaces but not when the dimension is at least four. The case of threefolds remains mysterious but we now know that stable rationality - rationality after taking products with projective spaces - is not a deformation invariant.

(Joint with Kresch, Pirutka, and Tschinkel)

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