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- W2565006057 abstract "Let C : f (x,y) = an(x)y+ · · ·+a1(x)y+a0(x) = 0 be a complex plane algebraic curve and F(z1,z2,z3) = z3 f (z1/z3,z2/z3) be its homogenization where d is the total degree of the curve. An algebraic curve defines an n-sheeted covering y(x) of the Riemann sphere C∪{∞}. A branch point of this covering is a point x = b ∈ C such that y(x) does not return to its original value when analytically continued around a small circle about x = b. That is, if y(x) has any branch points then y(x) is multi-valued. The Riemann surface Γ of the curve C is a one-dimensional complex manifold where y(x) is single-valued. Furthermore, it is a result from topology that the Riemann surface of an algebraic curve is homeomorphic to a genus g compact, connected surface." @default.
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- W2565006057 date "2010-01-01" @default.
- W2565006057 modified "2023-09-24" @default.
- W2565006057 title "Computing Bitangents of Quartics using Riemann Theta Functions" @default.
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