Linear relations among holomorphic quadratic differentials and induced Siegel’s metric on Mg
نویسندگان
چکیده
We derive the (g − 2)(g − 3)/2 linearly independent relations among the products of pairs in a basis of holomorphic abelian differentials in the case of compact non-hyperelliptic Riemann surfaces of genus g ≥ 4. By the Kodaira-Spencer map this leads to the modular invariant metric on the moduli space induced by the Siegel metric.
منابع مشابه
LINEAR RELATIONS AMONG HOLOMORPHIC QUADRATIC DIFFERENTIALS AND INDUCED SIEGEL’S METRIC ON Mg MARCO MATONE AND ROBERTO VOLPATO
We derive the explicit form of the (g − 2)(g − 3)/2 linearly independent relations among the products of pairs in a basis of holomorphic abelian differentials in the case of canonical curves of genus g ≥ 4. It turns out that Petri’s relations remarkably match in determinantal conditions. We explicitly express the volume form on the moduli space M̂g of canonical curves induced by the Siegel metri...
متن کامل2 7 Ju n 20 05 Linear relations among holomorphic quadratic differentials and induced Siegel ’ s metric
We derive the (g − 2)(g − 3)/2 linearly independent relations among the products of pairs in a basis of holomorphic abelian differentials in the case of compact non-hyperelliptic Riemann surfaces of genus g ≥ 4. By the Kodaira-Spencer map this leads to the modular invariant metric on the moduli space induced by the Siegel metric.
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