Theorem: compact Riemann surface C_g has dim H^0(C_g, Omega^1) = g (algebraic-geometric invariant)

Layer 1 — Physicsin the integrable-systems-physics subtree

Theorem (Riemann-Roch genus-g holomorphic-differential canonical): on a compact Riemann surface C_g of genus g, the dimension of the space of holomorphic 1-forms equals g: dim H^0(C_g, Omega^1) = g. Hyperelliptic realization: y^2 =…

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Lax-pair spectral curve: L*psi = lambda*psi defines Riemann surface C_g with dim Omega^1(C_g) = g

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