Algebraic surfaces in positive characteristics: purely inseparable phenomena in curves and surfaces
"Customarily, the framework of algebraic geometry has been worked over an algebraically closed field of characteristic zero, say, over the complex number field. However, over a field of positive characteristics, many unpredictable phenomena arise where analyses will lead to further developments...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific
2020
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| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | "Customarily, the framework of algebraic geometry has been worked over an algebraically closed field of characteristic zero, say, over the complex number field. However, over a field of positive characteristics, many unpredictable phenomena arise where analyses will lead to further developments. In the present book, we consider first the forms of the affine line or the additive group, classification of such forms and detailed analysis. The forms of the affine line considered over the function field of an algebraic curve define the algebraic surfaces with fibrations by curves with moving singularities. These fibrations are investigated via the Mordell-Weil groups, which are originally introduced for elliptic fibrations. This is the first book which explains the phenomena arising from purely inseparable coverings and Artin-Schreier coverings. In most cases, the base surfaces are rational, hence the covering surfaces are unirational. There exists a vast, unexplored world of unirational surfaces. In this book, we explain the Frobenius sandwiches as examples of unirational surfaces. Rational double points in positive characteristics are treated in detail with concrete computations. These kinds of computations are not found in current literature. Readers, by following the computations line after line, will not only understand the peculiar phenomena in positive characteristics, but also understand what are crucial in computations. This type of experience will lead the readers to find the unsolved problems by themselves"--Publisher's website |
| Beschreibung: | 1 Online-Ressource (xiii, 441 Seiten) |
| ISBN: | 9789811215216 |
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| 100 | 1 | |a Miyanishi, Masayoshi |d 1940- |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Algebraic surfaces in positive characteristics |b purely inseparable phenomena in curves and surfaces |c by Masayoshi Miyanishi, Hiroyuki Ito |
| 264 | 1 | |a Singapore |b World Scientific |c 2020 | |
| 300 | |a 1 Online-Ressource (xiii, 441 Seiten) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
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| 520 | |a "Customarily, the framework of algebraic geometry has been worked over an algebraically closed field of characteristic zero, say, over the complex number field. However, over a field of positive characteristics, many unpredictable phenomena arise where analyses will lead to further developments. In the present book, we consider first the forms of the affine line or the additive group, classification of such forms and detailed analysis. The forms of the affine line considered over the function field of an algebraic curve define the algebraic surfaces with fibrations by curves with moving singularities. These fibrations are investigated via the Mordell-Weil groups, which are originally introduced for elliptic fibrations. This is the first book which explains the phenomena arising from purely inseparable coverings and Artin-Schreier coverings. In most cases, the base surfaces are rational, hence the covering surfaces are unirational. There exists a vast, unexplored world of unirational surfaces. In this book, we explain the Frobenius sandwiches as examples of unirational surfaces. Rational double points in positive characteristics are treated in detail with concrete computations. These kinds of computations are not found in current literature. Readers, by following the computations line after line, will not only understand the peculiar phenomena in positive characteristics, but also understand what are crucial in computations. This type of experience will lead the readers to find the unsolved problems by themselves"--Publisher's website | ||
| 650 | 4 | |a Surfaces, Algebraic | |
| 650 | 4 | |a Curves, Algebraic | |
| 650 | 4 | |a Characteristic classes | |
| 700 | 1 | |a Ito, Hiroyuki |d 1966- |e Sonstige |4 oth | |
| 856 | 4 | 0 | |u https://www.worldscientific.com/worldscibooks/10.1142/11690#t=toc |x Verlag |z URL des Erstveröffentlichers |3 Volltext |
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Datensatz im Suchindex
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| author | Miyanishi, Masayoshi 1940- |
| author_facet | Miyanishi, Masayoshi 1940- |
| author_role | aut |
| author_sort | Miyanishi, Masayoshi 1940- |
| author_variant | m m mm |
| building | Verbundindex |
| bvnumber | BV047124305 |
| collection | ZDB-124-WOP |
| ctrlnum | (ZDB-124-WOP)00011690 (OCoLC)1237587467 (DE-599)BVBBV047124305 |
| dewey-full | 516.352 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.352 |
| dewey-search | 516.352 |
| dewey-sort | 3516.352 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV047124305 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T16:30:25Z |
| indexdate | 2024-07-10T09:03:18Z |
| institution | BVB |
| isbn | 9789811215216 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032530545 |
| oclc_num | 1237587467 |
| open_access_boolean | |
| physical | 1 Online-Ressource (xiii, 441 Seiten) |
| psigel | ZDB-124-WOP |
| publishDate | 2020 |
| publishDateSearch | 2020 |
| publishDateSort | 2020 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Miyanishi, Masayoshi 1940- Verfasser aut Algebraic surfaces in positive characteristics purely inseparable phenomena in curves and surfaces by Masayoshi Miyanishi, Hiroyuki Ito Singapore World Scientific 2020 1 Online-Ressource (xiii, 441 Seiten) txt rdacontent c rdamedia cr rdacarrier "Customarily, the framework of algebraic geometry has been worked over an algebraically closed field of characteristic zero, say, over the complex number field. However, over a field of positive characteristics, many unpredictable phenomena arise where analyses will lead to further developments. In the present book, we consider first the forms of the affine line or the additive group, classification of such forms and detailed analysis. The forms of the affine line considered over the function field of an algebraic curve define the algebraic surfaces with fibrations by curves with moving singularities. These fibrations are investigated via the Mordell-Weil groups, which are originally introduced for elliptic fibrations. This is the first book which explains the phenomena arising from purely inseparable coverings and Artin-Schreier coverings. In most cases, the base surfaces are rational, hence the covering surfaces are unirational. There exists a vast, unexplored world of unirational surfaces. In this book, we explain the Frobenius sandwiches as examples of unirational surfaces. Rational double points in positive characteristics are treated in detail with concrete computations. These kinds of computations are not found in current literature. Readers, by following the computations line after line, will not only understand the peculiar phenomena in positive characteristics, but also understand what are crucial in computations. This type of experience will lead the readers to find the unsolved problems by themselves"--Publisher's website Surfaces, Algebraic Curves, Algebraic Characteristic classes Ito, Hiroyuki 1966- Sonstige oth https://www.worldscientific.com/worldscibooks/10.1142/11690#t=toc Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Miyanishi, Masayoshi 1940- Algebraic surfaces in positive characteristics purely inseparable phenomena in curves and surfaces Surfaces, Algebraic Curves, Algebraic Characteristic classes |
| title | Algebraic surfaces in positive characteristics purely inseparable phenomena in curves and surfaces |
| title_auth | Algebraic surfaces in positive characteristics purely inseparable phenomena in curves and surfaces |
| title_exact_search | Algebraic surfaces in positive characteristics purely inseparable phenomena in curves and surfaces |
| title_exact_search_txtP | Algebraic surfaces in positive characteristics purely inseparable phenomena in curves and surfaces |
| title_full | Algebraic surfaces in positive characteristics purely inseparable phenomena in curves and surfaces by Masayoshi Miyanishi, Hiroyuki Ito |
| title_fullStr | Algebraic surfaces in positive characteristics purely inseparable phenomena in curves and surfaces by Masayoshi Miyanishi, Hiroyuki Ito |
| title_full_unstemmed | Algebraic surfaces in positive characteristics purely inseparable phenomena in curves and surfaces by Masayoshi Miyanishi, Hiroyuki Ito |
| title_short | Algebraic surfaces in positive characteristics |
| title_sort | algebraic surfaces in positive characteristics purely inseparable phenomena in curves and surfaces |
| title_sub | purely inseparable phenomena in curves and surfaces |
| topic | Surfaces, Algebraic Curves, Algebraic Characteristic classes |
| topic_facet | Surfaces, Algebraic Curves, Algebraic Characteristic classes |
| url | https://www.worldscientific.com/worldscibooks/10.1142/11690#t=toc |
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