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.
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Produktdetaljer
ISBN
9781400872695
Publisert
2016
Utgiver
Vendor
Princeton University Press
Språk
Product language
Engelsk
Format
Product format
Digital bok
Forfatter