A converse of Riemann's theorem on Jacobian varieties
Thomas Kraemer (Humboldt-Universitaet zu Berlin)
Aula Beltrami - Thursday, June 6, 2019 h.16:30
Abstract. Jacobians of curves have been studied a lot since Riemann’s
theorem, which says that their theta divisor is a sum of copies of the
curve. Similarly, for intermediate Jacobians of smooth cubic threefolds
Clemens and Griffiths showed that the theta divisor is a sum of two
copies of the Fano surface of lines on the threefold. We prove that in
both cases these are the only decompositions of the theta divisor,
extending previous results of Casalaina-Martin, Popa and Schreieder. Our
ideas apply to a much wider context and only rely on the decomposition
theorem for perverse sheaves and some representation theory.
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