A01=Robert C. Gunning
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Algebraic curve
Algebraic geometry
Algebraic operation
Algebraic variety
Analytic continuation
Analytic function
Analytic manifold
Author_Robert C. Gunning
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Bernhard Riemann
Category1=Non-Fiction
Category=PBKD
Category=PBMP
Cauchy's integral formula
Chern class
Clifford's theorem
Cohomology
Cohomology ring
Combinatorics
Commutative property
Compact Riemann surface
Complex analysis
Complex manifold
Complex multiplication
Complex projective space
Complex torus
COP=United States
Cotangent space
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Diagram (category theory)
Differential form
Differential of the first kind
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Equation
Existential quantification
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Group homomorphism
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Identity theorem
Induced homomorphism
Inner automorphism
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Irreducible component
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Line bundle
Linear map
Linear space (geometry)
Mathematical induction
Meromorphic function
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Open set
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Parity (mathematics)
Pole (complex analysis)
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Principal part
Projective line
Projective space
Projective variety
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Quotient space (topology)
Riemann sphere
Riemann surface
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softlaunch
Special case
Submanifold
Subset
Tangent bundle
Tangent space
Theorem
Topological space
Torelli theorem
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Vector space
Product details
- ISBN 9780691646169
- Weight: 454g
- Dimensions: 152 x 235mm
- Publication Date: 19 Apr 2016
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Hardback
- Language: English
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A sequel to Lectures on Riemann Surfaces (Mathematical Notes, 1966), this volume continues the discussion of the dimensions of spaces of holomorphic cross-sections of complex line bundles over compact Riemann surfaces. Whereas the earlier treatment was limited to results obtainable chiefly by one-dimensional methods, the more detailed analysis presented here requires the use of various properties of Jacobi varieties and of symmetric products of Riemann surfaces, and so serves as a further introduction to these topics as well. The first chapter consists of a rather explicit description of a canonical basis for the Abelian differentials on a marked Riemann surface, and of the description of the canonical meromorphic differentials and the prime function of a marked Riemann surface. Chapter 2 treats Jacobi varieties of compact Riemann surfaces and various subvarieties that arise in determining the dimensions of spaces of holomorphic cross-sections of complex line bundles.
In Chapter 3, the author discusses the relations between Jacobi varieties and symmetric products of Riemann surfaces relevant to the determination of dimensions of spaces of holomorphic cross-sections of complex line bundles. The final chapter derives Torelli's theorem following A. Weil, but in an analytical context. Originally published in 1973. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
