Riemann Surfaces and Generalized Theta Functions:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1976
|
| Schriftenreihe: | Ergebnisse der Mathematik und ihrer Grenzgebiete, A Series of Modern Surveys in Mathematics
91 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The investigation of the relationships between compact Riemann surfaces (al gebraic curves) and their associated complex tori (Jacobi varieties) has long been basic to the study both of Riemann surfaces and of complex tori. A Riemann surface is naturally imbedded as an analytic submanifold in its associated torus; and various spaces of linear equivalence elasses of divisors on the surface (or equivalently spaces of analytic equivalence elasses of complex line bundies over the surface), elassified according to the dimensions of the associated linear series (or the dimensions of the spaces of analytic cross-sections), are naturally realized as analytic subvarieties of the associated torus. One of the most fruitful of the elassical approaches to this investigation has been by way of theta functions. The space of linear equivalence elasses of positive divisors of order g -1 on a compact connected Riemann surface M of genus g is realized by an irreducible (g -1)-dimensional analytic subvariety, an irreducible hypersurface, of the associated g-dimensional complex torus J(M); this hyper 1 surface W- r;;;, J(M) is the image of the natural mapping Mg- -+J(M), and is g 1 1 birationally equivalent to the (g -1)-fold symmetric product Mg- jSg-l of the Riemann surface M. |
| Beschreibung: | 1 Online-Ressource (XII, 168 p) |
| ISBN: | 9783642663826 9783642663840 |
| ISSN: | 0071-1136 |
| DOI: | 10.1007/978-3-642-66382-6 |
Internformat
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| 245 | 1 | 0 | |a Riemann Surfaces and Generalized Theta Functions |c by Robert C. Gunning |
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| 500 | |a The investigation of the relationships between compact Riemann surfaces (al gebraic curves) and their associated complex tori (Jacobi varieties) has long been basic to the study both of Riemann surfaces and of complex tori. A Riemann surface is naturally imbedded as an analytic submanifold in its associated torus; and various spaces of linear equivalence elasses of divisors on the surface (or equivalently spaces of analytic equivalence elasses of complex line bundies over the surface), elassified according to the dimensions of the associated linear series (or the dimensions of the spaces of analytic cross-sections), are naturally realized as analytic subvarieties of the associated torus. One of the most fruitful of the elassical approaches to this investigation has been by way of theta functions. The space of linear equivalence elasses of positive divisors of order g -1 on a compact connected Riemann surface M of genus g is realized by an irreducible (g -1)-dimensional analytic subvariety, an irreducible hypersurface, of the associated g-dimensional complex torus J(M); this hyper 1 surface W- r;;;, J(M) is the image of the natural mapping Mg- -+J(M), and is g 1 1 birationally equivalent to the (g -1)-fold symmetric product Mg- jSg-l of the Riemann surface M. | ||
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Datensatz im Suchindex
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| author | Gunning, Robert C. |
| author_facet | Gunning, Robert C. |
| author_role | aut |
| author_sort | Gunning, Robert C. |
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| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-66382-6 |
| format | Electronic eBook |
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| id | DE-604.BV042422906 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:12Z |
| institution | BVB |
| isbn | 9783642663826 9783642663840 |
| issn | 0071-1136 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027858323 |
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| physical | 1 Online-Ressource (XII, 168 p) |
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| series2 | Ergebnisse der Mathematik und ihrer Grenzgebiete, A Series of Modern Surveys in Mathematics |
| spelling | Gunning, Robert C. Verfasser aut Riemann Surfaces and Generalized Theta Functions by Robert C. Gunning Berlin, Heidelberg Springer Berlin Heidelberg 1976 1 Online-Ressource (XII, 168 p) txt rdacontent c rdamedia cr rdacarrier Ergebnisse der Mathematik und ihrer Grenzgebiete, A Series of Modern Surveys in Mathematics 91 0071-1136 The investigation of the relationships between compact Riemann surfaces (al gebraic curves) and their associated complex tori (Jacobi varieties) has long been basic to the study both of Riemann surfaces and of complex tori. A Riemann surface is naturally imbedded as an analytic submanifold in its associated torus; and various spaces of linear equivalence elasses of divisors on the surface (or equivalently spaces of analytic equivalence elasses of complex line bundies over the surface), elassified according to the dimensions of the associated linear series (or the dimensions of the spaces of analytic cross-sections), are naturally realized as analytic subvarieties of the associated torus. One of the most fruitful of the elassical approaches to this investigation has been by way of theta functions. The space of linear equivalence elasses of positive divisors of order g -1 on a compact connected Riemann surface M of genus g is realized by an irreducible (g -1)-dimensional analytic subvariety, an irreducible hypersurface, of the associated g-dimensional complex torus J(M); this hyper 1 surface W- r;;;, J(M) is the image of the natural mapping Mg- -+J(M), and is g 1 1 birationally equivalent to the (g -1)-fold symmetric product Mg- jSg-l of the Riemann surface M. Mathematics Mathematics, general Mathematik Riemannsche Fläche (DE-588)4049991-1 gnd rswk-swf Thetafunktion (DE-588)4185175-4 gnd rswk-swf Riemannsche Fläche (DE-588)4049991-1 s 1\p DE-604 Thetafunktion (DE-588)4185175-4 s 2\p DE-604 https://doi.org/10.1007/978-3-642-66382-6 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Gunning, Robert C. Riemann Surfaces and Generalized Theta Functions Mathematics Mathematics, general Mathematik Riemannsche Fläche (DE-588)4049991-1 gnd Thetafunktion (DE-588)4185175-4 gnd |
| subject_GND | (DE-588)4049991-1 (DE-588)4185175-4 |
| title | Riemann Surfaces and Generalized Theta Functions |
| title_auth | Riemann Surfaces and Generalized Theta Functions |
| title_exact_search | Riemann Surfaces and Generalized Theta Functions |
| title_full | Riemann Surfaces and Generalized Theta Functions by Robert C. Gunning |
| title_fullStr | Riemann Surfaces and Generalized Theta Functions by Robert C. Gunning |
| title_full_unstemmed | Riemann Surfaces and Generalized Theta Functions by Robert C. Gunning |
| title_short | Riemann Surfaces and Generalized Theta Functions |
| title_sort | riemann surfaces and generalized theta functions |
| topic | Mathematics Mathematics, general Mathematik Riemannsche Fläche (DE-588)4049991-1 gnd Thetafunktion (DE-588)4185175-4 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik Riemannsche Fläche Thetafunktion |
| url | https://doi.org/10.1007/978-3-642-66382-6 |
| work_keys_str_mv | AT gunningrobertc riemannsurfacesandgeneralizedthetafunctions |