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Geometry of moduli spaces of rational curves

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If you have a question about this talk, please contact Helen Innes.

Recently Graber, Harris and Starr proved that any family of rationally connected projective varieties over a smooth curve has a section. A complex projective variety (or manifold) M is rationally connected when every two points in M lie on a rational curve in M. We will explain a generalization of this result, joint with Jason Starr, to the case when the base of the family is a surface. We will mention the analogy with Tsen’s theorem and the connection with the period-index problem for Brauer groups.

This talk is part of the Kuwait Foundation Lectures series.

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