Classical Theory of Compact Riemann Surfaces |
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A-periods a-place Abel's theorem abelian algebraic function B₁ canonical divisor closed curve conformal equivalence constants Conversely COROLLARY cycle define deg dz differential of second dīm dim or deg Dirichlet principle disc dz/z elliptic entials finite number fixed point follows formula function f fundamental polygon genus hence dim Hodge Hodge theorem holomorphic differ holomorphic differential holomorphic quadratic differentials integral inversion theorem kernel L(or LEMMA linear meromorphic differential meromorphic function morphic neighborhood non-constant meromorphic function non-zero normalized differential number of poles one-form one-one period relations pole of order Proof proved quadratic differentials rational function real harmonic residue RESIDUE THEOREM resp fn result Riemann surface Riemann-Roch theorem satisfying second kind singular space of holomorphic sphere Suppose topology torus triangulation uniformizing variable vanish whole number wp(z z-sphere zeros and poles Σο στ Σω