| 书目名称 | Resolution of Curve and Surface Singularities in Characteristic Zero | | 编辑 | K. Kiyek,J. L. Vicente | | 视频video | | | 丛书名称 | Algebra and Applications | | 图书封面 |  | | 描述 | The Curves The Point of View of Max Noether Probably the oldest references to the problem of resolution of singularities are found in Max Noether‘s works on plane curves [cf. [148], [149]]. And probably the origin of the problem was to have a formula to compute the genus of a plane curve. The genus is the most useful birational invariant of a curve in classical projective geometry. It was long known that, for a plane curve of degree n having l m ordinary singular points with respective multiplicities ri, i E {1, . . . , m}, the genus p of the curve is given by the formula = (n - l)(n - 2) _ ~ "r. (r. _ 1) P 2 2 L. . ,. •• . Of course, the problem now arises: how to compute the genus of a plane curve having some non-ordinary singularities. This leads to the natural question: can we birationally transform any (singular) plane curve into another one having only ordinary singularities? The answer is positive. Let us give a flavor (without proofs) 2 on how Noether did it • To solve the problem, it is enough to consider a special kind of Cremona trans formations, namely quadratic transformations of the projective plane. Let ~ be a linear system of conics with three non-collinear base po | | 出版日期 | Book 2004 | | 关键词 | Abelian group; Blowing up; Dimension; Divisor; Grad; algebraic geometry; brandonwiskunde; commutative algeb | | 版次 | 1 | | doi | https://doi.org/10.1007/978-1-4020-2029-2 | | isbn_softcover | 978-90-481-6573-5 | | isbn_ebook | 978-1-4020-2029-2Series ISSN 1572-5553 Series E-ISSN 2192-2950 | | issn_series | 1572-5553 | | copyright | Springer Science+Business Media New York 2004 |
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发表于 2025-3-21 16:53:49
