Ebook: Compact Riemann Surfaces

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Content:
Front Matter....Pages i-v
Algebraic functions....Pages 3-7
Riemann Surfaces....Pages 8-11
The Sheaf of Germs of Holomorphic Functions....Pages 12-14
The Riemann Surface of an Algebraic Function....Pages 15-16
Sheaves....Pages 17-26
Vector Bundles, Line Bundles and Divisors....Pages 27-31
Finiteness Theorems....Pages 32-37
The Dolbeault Isomorphism....Pages 38-42
Weyl’s Lemma and the Serre Duality Theorem....Pages 43-48
The Riemann-Roch Theorem and some Applications....Pages 49-57
Further Properties of Compact Riemann Surfaces....Pages 58-62
Hyperelliptic Curves and the Canonical Map....Pages 63-65
Some Geometry of Curves in Projective Space....Pages 66-76
Bilinear Relations....Pages 77-83
The Jacobian and Abel’s Theorem....Pages 84-90
The Riemann Theta Function....Pages 91-96
The Theta Divisor....Pages 97-105
Torelli’s Theorem....Pages 106-110
Riemann’s Theorem on the Singularities of ?....Pages 111-118
Back Matter....Pages 119-120

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Content:
Front Matter....Pages i-v
Algebraic functions....Pages 3-7
Riemann Surfaces....Pages 8-11
The Sheaf of Germs of Holomorphic Functions....Pages 12-14
The Riemann Surface of an Algebraic Function....Pages 15-16
Sheaves....Pages 17-26
Vector Bundles, Line Bundles and Divisors....Pages 27-31
Finiteness Theorems....Pages 32-37
The Dolbeault Isomorphism....Pages 38-42
Weyl’s Lemma and the Serre Duality Theorem....Pages 43-48
The Riemann-Roch Theorem and some Applications....Pages 49-57
Further Properties of Compact Riemann Surfaces....Pages 58-62
Hyperelliptic Curves and the Canonical Map....Pages 63-65
Some Geometry of Curves in Projective Space....Pages 66-76
Bilinear Relations....Pages 77-83
The Jacobian and Abel’s Theorem....Pages 84-90
The Riemann Theta Function....Pages 91-96
The Theta Divisor....Pages 97-105
Torelli’s Theorem....Pages 106-110
Riemann’s Theorem on the Singularities of ?....Pages 111-118
Back Matter....Pages 119-120
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