Torelli Theorem for the Moduli Spaces of Connections on a Riemann Surface
نویسنده
چکیده
Let (X , x0) be any one–pointed compact connected Riemann surface of genus g, with g ≥ 3. Fix two mutually coprime integers r > 1 and d. Let MX denote the moduli space parametrizing all logarithmic SL(r, C)–connections, singular over x0, on vector bundles over X of degree d. We prove that the isomorphism class of the variety MX determines the Riemann surface X uniquely up to an isomorphism, although the biholomorphism class of MX is known to be independent of the complex structure of X . The isomorphism class of the variety MX is independent of the point x0 ∈ X . A similar result is proved for the moduli space parametrizing logarithmic GL(r, C)–connections, singular over x0, on vector bundles over X of degree d.
منابع مشابه
TORELLI THEOREM FOR MODULI SPACES OF SL(r,C)–CONNECTIONS ON A COMPACT RIEMANN SURFACE
Let X be any compact connected Riemann surface of genus g, with g ≥ 3. For any r ≥ 2, let MX denote the moduli space of holomorphic SL(r, C)–connections over X . It is known that the biholomorphism class of the complex variety MX is independent of the complex structure of X . If g = 3, then we assume that r ≥ 3. We prove that the isomorphism class of the variety MX determines the Riemann surfac...
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