Canonical measures on the moduli spaces of compact Riemann surfaces
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We study some explicit relations between the canonical line bundle and the Hodge bundle over moduli spaces for low genus. This leads to a natural measure on the moduli space of every genus which is related to the Siegel symplectic metric on Siegel upper half-space as well as to the Hodge metric on the Hodge bundle.
KeywordsCanonical measures moduli spaces compact Riemann surfaces Hodge bundle Siegel symplectic metric
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