Fano hypersurfaces with large degrees of irrationality

Fano hypersurfaces with large degrees of irrationality

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Nathan Chen, Stony Brook University

Zoom link:  https://princeton.zoom.us/j/91248028438

 

Given a smooth projective variety, it is natural to ask (1) How can we determine when it is rational? and (2) If it is not rational, can we measure how far it is from being rational? When the variety is a smooth hypersurface in projective space, these questions have attracted a great deal of attention both classically and recently. In joint work with David Stapleton, we show that smooth Fano hypersurfaces of large dimension can have arbitrarily large degrees of irrationality, i.e. they can be arbitrarily far from being rational. Time permitting, I will also explain recent progress on complete intersections in codimension 2.