Algebraic Surfaces In Positive Characteristics: Purely Inseparable Phenomena In Curves And Surfaces

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Masayoshi Miyanishi (Univ Of Osaka, Japan) Hiroyuki Ito (Tokyo Univ Of Sci, Japan)

Algebraic Surfaces In Positive Characteristics

Purely Inseparable Phenomena In Curves And Surfaces

Masayoshi Miyanishi (Univ Of Osaka, Japan), Hiroyuki Ito (Tokyo Univ Of Sci, Japan)

$248.99

Hardback

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English

World Scientific Publishing Co Pte Ltd
30 June 2020

Algebraic geometry

Summary
Details

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.

By: Masayoshi Miyanishi (Univ Of Osaka Japan), Hiroyuki Ito (Tokyo Univ Of Sci, Japan)
Imprint: World Scientific Publishing Co Pte Ltd
Country of Publication: Singapore
ISBN: 9789811215209
ISBN 10: 9811215200
Pages: 456
Publication Date: 30 June 2020
Audience: College/higher education , Professional and scholarly , Primary , Undergraduate
Format: Hardback
Publisher's Status: Active

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Algebraic Surfaces In Positive Characteristics

Purely Inseparable Phenomena In Curves And Surfaces

Masayoshi Miyanishi (Univ Of Osaka, Japan), Hiroyuki Ito (Tokyo Univ Of Sci, Japan)

$248.99

Hardback

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