A Note on Hyperelliptic Curves
Copyright policy )A Note on Hyperelliptic Curves
If \(C\) is a Riemann surface of genus one or hyperelliptic Riemann surface of genus \(\geq 2\), then \(C\) admits a map \(p: C\to P^ 1\) of degree 2 branched over \(2g+2\) points. \(p\) is unique up to action of \(PGL_ 2(C)\) on \(P^ 1\), and translation of \(C\) if genus\((C)=1\). The author proves that there is no universal family of such maps parametrized by the set \(X_{2g+2}\) of \(2g+g\) unordered distinct points of \(P^ 1\).
Families, moduli of curves (analytic), hyperelliptic Riemann surface, universal family of maps, branched covering over the 2-sphere, Riemann surface of genus one, Compact Riemann surfaces and uniformization, Low-dimensional topology of special (e.g., branched) coverings
Families, moduli of curves (analytic), hyperelliptic Riemann surface, universal family of maps, branched covering over the 2-sphere, Riemann surface of genus one, Compact Riemann surfaces and uniformization, Low-dimensional topology of special (e.g., branched) coverings
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