Non-hyperelliptic Riemann surfaces
نویسندگان
چکیده
منابع مشابه
On p-hyperelliptic Involutions of Riemann Surfaces
A compact Riemann surface X of genus g > 1 is said to be phyperelliptic if X admits a conformal involution ρ, called a p-hyperelliptic involution, for which X/ρ is an orbifold of genus p. Here we give a new proof of the well known fact that for g > 4p + 1, ρ is unique and central in the group of all automorphisms of X. Moreover we prove that every two p-hyperelliptic involutions commute for 3p ...
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A compact Riemann surface X of genus g > 1 is said to be a p-hyperelliptic if X admits a conformal involution ρ for which X/ρ has genus p. This notion is the particular case of so called cyclic (q, n)-gonal surface which is defined as the one admitting a conformal automorphism δ of order n such that X/δ has genus q. It is known that for g > 4p + 1, ρ is unique and so central in the automorphism...
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We consider the vortex equations for a U(n) gauge field A coupled to a Higgs field φ with values on the n × n matrices. It is known that when these equations are defined on a compact Riemann surface Σ, their moduli space of solutions is closely related to a moduli space of τ -stable holomorphic n-pairs on that surface. Using this fact and a local factorization result for the matrix φ, we show t...
متن کاملPhysically Realistic Solutions to the Ernst Equation on Hyperelliptic Riemann Surfaces
A class of solutions to the Ernst equation (the stationary axisymmetric Einstein equations in vacuum) is discussed which is constructed via Riemann–Hilbert techniques on hyperelliptic Riemann surfaces. We identify a physically interesting subclass where the Ernst potential is everywhere regular except at a closed surface which might be identified with the surface of a body of revolution. The co...
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ژورنال
عنوان ژورنال: Journal of Differential Geometry
سال: 1969
ISSN: 0022-040X
DOI: 10.4310/jdg/1214428821