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Jacobians of isospectral Riemann surfaces
Eran Makover, 19 février 2008, 11h15, MA 12 Abstract: Riemann surfaces are an important example for a class of manifold in which the relation between geometric properties of the manifold and their spectra of the Laplace operator has been studied extensively. One of the important invariant of compact Riemann surface is its Jacobian. We are looking at the relationship between Jacobians of isospectral Riemann surfaces. In the case of isospectral surfaces arise from the Sunada construction we can construct an explicit transplantation between the two Jacobian. This enables us to investigate the relationship between the Jacobians. We can show that as a principally polarized abelian variety they lie in the same $Sp(2g,k)$-orbit, where k is some finite algebraic extension field of the rational field $\mathbf{Q}$. Joint with Carolyn Gordon and David Webb. |
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