Local analytic geometry
This book provides, for use in a graduate course or for self-study by graduate students, a well-motivated treatment of several topics, especially the following: (1) algebraic treatment of several complex variables; (2) geometric approach to algebraic geometry via analytic sets; (3) survey of local a...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
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World Scientific Pub. Co.
c2001
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| Schriftenreihe: | Pure and applied mathematics; a series of monographs and textbooks
14 |
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| 245 | 1 | 0 | |a Local analytic geometry |c Shreeram Shankar Abhyankar |
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| 490 | 0 | |a Pure and applied mathematics; a series of monographs and textbooks |v 14 | |
| 500 | |a Originally published: New York : Academic Press, c1964, in series Pure and applied mathematics (Academic Press) ; 14 | ||
| 520 | |a This book provides, for use in a graduate course or for self-study by graduate students, a well-motivated treatment of several topics, especially the following: (1) algebraic treatment of several complex variables; (2) geometric approach to algebraic geometry via analytic sets; (3) survey of local algebra; (4) survey of sheaf theory.The book has been written in the spirit of Weierstrass. Power series play the dominant role. The treatment, being algebraic, is not restricted to complex numbers, but remains valid over any complete-valued field. This makes it applicable to situations arising from number theory. When it is specialized to the complex case, connectivity and other topological properties come to the fore. In particular, via singularities of analytic sets, topological fundamental groups can be studied.In the transition from punctual to local, i.e. from properties at a point to properties near a point, the classical work of Osgood plays an important role. This gives rise to normic forms and the concept of the Osgoodian. Following Serre, the passage from local to global properties of analytic spaces is facilitated by introducing sheaf theory. Here the fundamental results are the coherence theorems of Oka and Cartan. They are followed by theory normalization due to Oka and Zariski in the analytic and algebraic cases, respectively | ||
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Datensatz im Suchindex
| _version_ | 1819301212778921986 |
|---|---|
| any_adam_object | |
| author | Abhyankar, Shreeram Shankar |
| author_facet | Abhyankar, Shreeram Shankar |
| author_role | aut |
| author_sort | Abhyankar, Shreeram Shankar |
| author_variant | s s a ss ssa |
| building | Verbundindex |
| bvnumber | BV044636099 |
| classification_rvk | SK 240 |
| collection | ZDB-124-WOP |
| ctrlnum | (ZDB-124-WOP)00004433 (OCoLC)1012691499 (DE-599)BVBBV044636099 |
| dewey-full | 516.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3 |
| dewey-search | 516.3 |
| dewey-sort | 3516.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV044636099 |
| illustrated | Illustrated |
| indexdate | 2024-12-24T06:13:57Z |
| institution | BVB |
| isbn | 9789812810342 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030034071 |
| oclc_num | 1012691499 |
| open_access_boolean | |
| owner | DE-92 |
| owner_facet | DE-92 |
| physical | xv, 488 p. ill |
| psigel | ZDB-124-WOP ZDB-124-WOP FHN_PDA_WOP |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | World Scientific Pub. Co. |
| record_format | marc |
| series2 | Pure and applied mathematics; a series of monographs and textbooks |
| spelling | Abhyankar, Shreeram Shankar Verfasser aut Local analytic geometry Shreeram Shankar Abhyankar Singapore World Scientific Pub. Co. c2001 xv, 488 p. ill txt rdacontent c rdamedia cr rdacarrier Pure and applied mathematics; a series of monographs and textbooks 14 Originally published: New York : Academic Press, c1964, in series Pure and applied mathematics (Academic Press) ; 14 This book provides, for use in a graduate course or for self-study by graduate students, a well-motivated treatment of several topics, especially the following: (1) algebraic treatment of several complex variables; (2) geometric approach to algebraic geometry via analytic sets; (3) survey of local algebra; (4) survey of sheaf theory.The book has been written in the spirit of Weierstrass. Power series play the dominant role. The treatment, being algebraic, is not restricted to complex numbers, but remains valid over any complete-valued field. This makes it applicable to situations arising from number theory. When it is specialized to the complex case, connectivity and other topological properties come to the fore. In particular, via singularities of analytic sets, topological fundamental groups can be studied.In the transition from punctual to local, i.e. from properties at a point to properties near a point, the classical work of Osgood plays an important role. This gives rise to normic forms and the concept of the Osgoodian. Following Serre, the passage from local to global properties of analytic spaces is facilitated by introducing sheaf theory. Here the fundamental results are the coherence theorems of Oka and Cartan. They are followed by theory normalization due to Oka and Zariski in the analytic and algebraic cases, respectively Geometry, Analytic Functional analysis Polynom (DE-588)4046711-9 gnd rswk-swf Analytische Geometrie (DE-588)4001867-2 gnd rswk-swf Analytische Menge (DE-588)4142351-3 gnd rswk-swf Analytische Funktion (DE-588)4142348-3 gnd rswk-swf Analytische Geometrie (DE-588)4001867-2 s 1\p DE-604 Polynom (DE-588)4046711-9 s 2\p DE-604 Analytische Funktion (DE-588)4142348-3 s 3\p DE-604 Analytische Menge (DE-588)4142351-3 s 4\p DE-604 Erscheint auch als Druck-Ausgabe 9789810245054 Erscheint auch als Druck-Ausgabe 981024505X http://www.worldscientific.com/worldscibooks/10.1142/4596#t=toc Verlag URL des Erstveroeffentlichers 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 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Abhyankar, Shreeram Shankar Local analytic geometry Geometry, Analytic Functional analysis Polynom (DE-588)4046711-9 gnd Analytische Geometrie (DE-588)4001867-2 gnd Analytische Menge (DE-588)4142351-3 gnd Analytische Funktion (DE-588)4142348-3 gnd |
| subject_GND | (DE-588)4046711-9 (DE-588)4001867-2 (DE-588)4142351-3 (DE-588)4142348-3 |
| title | Local analytic geometry |
| title_auth | Local analytic geometry |
| title_exact_search | Local analytic geometry |
| title_full | Local analytic geometry Shreeram Shankar Abhyankar |
| title_fullStr | Local analytic geometry Shreeram Shankar Abhyankar |
| title_full_unstemmed | Local analytic geometry Shreeram Shankar Abhyankar |
| title_short | Local analytic geometry |
| title_sort | local analytic geometry |
| topic | Geometry, Analytic Functional analysis Polynom (DE-588)4046711-9 gnd Analytische Geometrie (DE-588)4001867-2 gnd Analytische Menge (DE-588)4142351-3 gnd Analytische Funktion (DE-588)4142348-3 gnd |
| topic_facet | Geometry, Analytic Functional analysis Polynom Analytische Geometrie Analytische Menge Analytische Funktion |
| url | http://www.worldscientific.com/worldscibooks/10.1142/4596#t=toc |
| work_keys_str_mv | AT abhyankarshreeramshankar localanalyticgeometry |