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Resolution of singularities of embedded algebraic surfaces

Abhyankar, S. S.



Resolution of singularities of embedded algebraic surfaces

Tác giả: Abhyankar, S. S.
Loại tài liệu: Sách, chuyên khảo, tuyển tập
Ký hiệu: Lv4164
Mã giá: 13AB
Nội dung tóm tắt: Xem chi tiết
The common solutions of a finite number of polynomial equations in a finite number of variables constitute an algebraic variety. The degrees of freedom of a moving point on the variety is the dimension of the variety. A one-dimensional variety is a curve and a two-dimensional variety is a surface. A three-dimensional variety may be called a solid. Most points of a variety are simple points. Singularities are special points, or points of multiplicity greater than one. Points of multiplicity two are double points, points of multiplicity three are triple points, and so on. A nodal point of a curve is a double point where the curve crosses itself, such as the alpha curve. Acusp is a double point where the curve has a beak. The vertex of a cone provides an example of a surface singularity. A reversible change of variables gives a birational transformation of a variety. Singularities: of a variety maybe resolved by birational transformations. The present book contains the geometric part of the proof of solid desingularization in characteristic p Z ,3,5 which I obtained in 1965; the algorithmic part is contained in my four previous articles 5 to 9; the book does contain an alternative simple version of the algorithm for characteristic zero; half of the book can also be used as an introduction to birational algebraic geometry.
Mục lục: Xem chi tiết
0 Introduction CHAPTER 1. Local Theory 1 Terminology and preliminaries 2 Resolvers and principalizers 3 Dominant character of a normal sequence 4 Unramified local extensions 5 Main results CHAPTER 2. Global Theory 6 Terminology and preliminaries 7 Global resolvers 8 Global principalizers 9 Main results CHAPTER 3. Some Cases of Three-Dimensional Birational Resolution 10 Uniformization of points of small multiplicity 11 Three-dimensional birational resolution over a ground field of characteristic zero 12 Existence of projective models having only points of small multiplicity 13 Three-dimensional birational resolution over an algebraically closed ground field of charateristic # 2,3,5 Appendix on Analytic Dessingularization in Characteristic Zero Bibliograpgy Additional Bibliograpgy Index of Notations Index of Definitons List of Corrections

Thông tin chi tiết

    Dạng tài liệu:Bản in
    Chỉ số ISBN:3-540-63719-2
    Ngôn ngữ:eng
    Mã giá:13AB
    Mã MSC:Đang cập nhật ...
    Tác giả:Abhyankar, S. S
    Nhan đề:Resolution of singularities of embedded algebraic surfaces
    Lần xuất bản:2
    Xuất bản, phát hành:H : Berlin , 1998
    Số trang:311;
    Kích thước:24 cm
    Từ Khóa:analytic desingularization , resolution of algebraic surface , resolution of singularities
    Bộ sách:Springer Monographs in Mathematics.

Thông tin xếp giá

  • ĐKCB: 1469150065816
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