## Riemann surfaces and generalized theta functions |

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### Contents

Complex Manifolds and Vector Bundles | 1 |

Riemann Surfaces | 17 |

Generalized Theta Functions | 39 |

Copyright | |

3 other sections not shown

### Common terms and phrases

Abelian differentials Abelian integral analytic line bundle analytic relatively automorphic analytic vector bundle analytically trivial automorphy of rank base point bundle homomorphism characteristic class characteristic matrix compact Riemann surface complex analytic function complex analytic line complex analytic mapping complex analytic relatively complex analytic subvariety complex analytic vector complex manifold complex tori conclude the proof consequence coordinate covering coordinate neighborhoods coordinate transformations Corollary defined described differential form differentials associated divisor element TeT exact sequence factor of auto factor of automorphy fixed points flat factor function of rank fundamental polygon hence isomorphic lattice subgroup linear linearly independent marked Riemann surface meromorphic function meromorphic Prym differentials morphy nonsingular open neighborhood path period matrix points zeM precisely Prym differentials associated Prym period rank g relatively automorphic function represent distinct points Riemann-Roch theorem satisfies scalar factor singularities space of complex theta factor theta function torus universal covering space vanishing vector space zero