Lectures on Riemann Surfaces : : Jacobi Varieties / / Robert C. Gunning.
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-di...
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Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2015] ©1973 |
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Gunning, Robert C., author. aut http://id.loc.gov/vocabulary/relators/aut Lectures on Riemann Surfaces : Jacobi Varieties / Robert C. Gunning. Princeton, NJ : Princeton University Press, [2015] ©1973 1 online resource (198 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Princeton Legacy Library ; 1238 Frontmatter -- Preface -- Contents -- § 1. Marked Riemann surfaces and their canonical differentials -- § 2. Jacobi varieties and their distinguished subvarieties -- § 3. Jacobi varieties and symmetric products of Riemann surfaces -- § 4. Intersections in Jacobi varieties and Torelli's theorem -- Appendix. On conditions ensuring that W2r≠ ⌀ -- Index of symbols -- Index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star 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. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 30. Aug 2021) Jacobi varieties. Riemann surfaces. MATHEMATICS / Geometry / Non-Euclidean. bisacsh Title is part of eBook package: De Gruyter Princeton Legacy Lib. eBook Package 1931-1979 9783110426847 Title is part of eBook package: De Gruyter Princeton Legacy Lib. eBook Package Science 9783110413595 Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999 9783110442496 print 9780691619255 https://doi.org/10.1515/9781400872695 https://www.degruyter.com/isbn/9781400872695 Cover https://www.degruyter.com/cover/covers/9781400872695.jpg |
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English |
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author |
Gunning, Robert C., Gunning, Robert C., |
spellingShingle |
Gunning, Robert C., Gunning, Robert C., Lectures on Riemann Surfaces : Jacobi Varieties / Princeton Legacy Library ; Frontmatter -- Preface -- Contents -- § 1. Marked Riemann surfaces and their canonical differentials -- § 2. Jacobi varieties and their distinguished subvarieties -- § 3. Jacobi varieties and symmetric products of Riemann surfaces -- § 4. Intersections in Jacobi varieties and Torelli's theorem -- Appendix. On conditions ensuring that W2r≠ ⌀ -- Index of symbols -- Index |
author_facet |
Gunning, Robert C., Gunning, Robert C., |
author_variant |
r c g rc rcg r c g rc rcg |
author_role |
VerfasserIn VerfasserIn |
author_sort |
Gunning, Robert C., |
title |
Lectures on Riemann Surfaces : Jacobi Varieties / |
title_sub |
Jacobi Varieties / |
title_full |
Lectures on Riemann Surfaces : Jacobi Varieties / Robert C. Gunning. |
title_fullStr |
Lectures on Riemann Surfaces : Jacobi Varieties / Robert C. Gunning. |
title_full_unstemmed |
Lectures on Riemann Surfaces : Jacobi Varieties / Robert C. Gunning. |
title_auth |
Lectures on Riemann Surfaces : Jacobi Varieties / |
title_alt |
Frontmatter -- Preface -- Contents -- § 1. Marked Riemann surfaces and their canonical differentials -- § 2. Jacobi varieties and their distinguished subvarieties -- § 3. Jacobi varieties and symmetric products of Riemann surfaces -- § 4. Intersections in Jacobi varieties and Torelli's theorem -- Appendix. On conditions ensuring that W2r≠ ⌀ -- Index of symbols -- Index |
title_new |
Lectures on Riemann Surfaces : |
title_sort |
lectures on riemann surfaces : jacobi varieties / |
series |
Princeton Legacy Library ; |
series2 |
Princeton Legacy Library ; |
publisher |
Princeton University Press, |
publishDate |
2015 |
physical |
1 online resource (198 p.) Issued also in print. |
contents |
Frontmatter -- Preface -- Contents -- § 1. Marked Riemann surfaces and their canonical differentials -- § 2. Jacobi varieties and their distinguished subvarieties -- § 3. Jacobi varieties and symmetric products of Riemann surfaces -- § 4. Intersections in Jacobi varieties and Torelli's theorem -- Appendix. On conditions ensuring that W2r≠ ⌀ -- Index of symbols -- Index |
isbn |
9781400872695 9783110426847 9783110413595 9783110442496 9780691619255 |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA333 |
callnumber-sort |
QA 3333 |
url |
https://doi.org/10.1515/9781400872695 https://www.degruyter.com/isbn/9781400872695 https://www.degruyter.com/cover/covers/9781400872695.jpg |
illustrated |
Not Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
515 - Analysis |
dewey-full |
515/.223 |
dewey-sort |
3515 3223 |
dewey-raw |
515/.223 |
dewey-search |
515/.223 |
doi_str_mv |
10.1515/9781400872695 |
oclc_num |
979905673 |
work_keys_str_mv |
AT gunningrobertc lecturesonriemannsurfacesjacobivarieties |
status_str |
n |
ids_txt_mv |
(DE-B1597)454628 (OCoLC)979905673 |
carrierType_str_mv |
cr |
hierarchy_parent_title |
Title is part of eBook package: De Gruyter Princeton Legacy Lib. eBook Package 1931-1979 Title is part of eBook package: De Gruyter Princeton Legacy Lib. eBook Package Science Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999 |
is_hierarchy_title |
Lectures on Riemann Surfaces : Jacobi Varieties / |
container_title |
Title is part of eBook package: De Gruyter Princeton Legacy Lib. eBook Package 1931-1979 |
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1806143624748990464 |
fullrecord |
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