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Weighted expansions for canonical desingularization

Abhyankar, S. S.

Berlin-Heidelberg-New York


Weighted expansions for canonical desingularization

Tác giả: Abhyankar, S. S.
Loại tài liệu: Sách, chuyên khảo, tuyển tập
Ký hiệu: Lv2905
Mã giá: 14AB
Nội dung tóm tắt: Xem chi tiết
We point out two major differences to Hironaka's famous proof. One is the visible change of the singularity in each step. The second is that this new proof does not use any induction on the dimension of the variety. Even if one takes the expansion for granted, the description of resolution given above was not quite correct. The final proof will use another iteration of this procedure. After expanding one equation, one can extract some coefficients. These coefficients have to be expanded again, then the coefficients of the coefficients, etc. This leads to the notion of a web, which is not treated here. After this rather crude description of a very complicated mechanism, we can indicate the content of the paper that follows. It contains the notation which is necessary to deal with the huge amount of information contained in the expansion. Then there is a proof for the existence of weighted initial forms in great generality, maybe more general than is needed for the purpose of resolution. Finally the existence of an expansion as indicated above is proved. ; With foreword by U. Orbanz.
Mục lục: Xem chi tiết
Foreword Preface 1. Notation 2. Semigroups 3. Strings 4. Semigroup strings with restrictions 5. Ordered semigroup strings with restrictions 6. Strings on rings 7. Indeterminate strings 8. Indeterminate strings with restrictions 9. Restricted degree and order for indeterminate strings 10. Indexing strings 11. Nets 12. Semigroup nets with restrictions 13. Ordered semigroup nets with restrictions 14. Nets on rings 15. Indeterminate nets 16. Indeterminate nets with restrictions 17. Restricted degree and order for indeterminate nets 18. Prechips 19. Isobars for prechips and Premonic polynomials 20. Substitutions 21. Substitutions with restrictions 22. Coordinate nets and Monic polynomials 23. Graded ring of a ring at an ideal 24. Graded ring of a ring 25. Graded rings at strings and nets and the notions of separatedness and regularity for strings and nets 26. Inner products and further notions of separatedness and regularity for strings 27. Inner products and further notions of separatedness and regularity for nets 28. Weighted isobars and weighted initial forms initial forms for regular strings 29. Initial forms for regular strings and nets 30. Protochips and parachips 31. N-support of an indexing string for 2 =<N =<6 32. Prescales 33. Deriyed prescales 34. Supports of prescales 35. Protoscales 36. Inner products for protoscales 37. Scales and isobars 38. Properties of derived prescales 39. Isobars for derived scales 40. Isobars and initial forms for scales 41. Initial forms for scales and regular nets 42. Isobars for protochips 43. Initial forms for protochips and monic polynomials Index of definitions Index of notations

Thông tin chi tiết

    Dạng tài liệu:Bản in
    Chỉ số ISBN:3-540-11195-6
    Ngôn ngữ:eng
    Mã giá:14AB
    Mã MSC:Đang cập nhật ...
    Tác giả:Abhyankar, S. S
    Nhan đề:Weighted expansions for canonical desingularization
    Xuất bản, phát hành:H : Berlin-Heidelberg-New York , 1982
    Số trang:236;
    Kích thước:24 cm
    Từ Khóa:exceptional divisor , expansion , quadratic transformations , singular points
    Bộ sách:Lecture Notes in Mathematics. 910.

Thông tin xếp giá

  • ĐKCB: 1469150051642
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