Algebraic Surfaces in Positive Characteristics:Purely Inseparable Phenomena in Curves and Surfaces

正特性代数曲面:曲线和表面完全不可分离的现象

几何学

原   价:
1499.00
售   价:
1124.00
发货周期:预计3-5周发货
出  版 社
出版时间
2020年06月30日
装      帧
精装
ISBN
9789811215209
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页      码
450 pp
语      种
英文
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图书简介
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 characterisitcs, but also understand what are crucial in computations. This type of experience will lead to finding of unsolved problems by the readers themselves. Key Features: ○The mainstreams of arguments are explained, followed by computations ○Several concrete examples are given to elucidate the stated results ○All in all, the present book is more for practice than learning a general theory
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