Resolution of Curve and Surface Singularities in Characteristic Zero is popular PDF and ePub book, written by K. Kiyek in 2012-09-11, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Resolution of Curve and Surface Singularities in Characteristic Zero can be Read Online from any device for your convenience.
Resolution of Curve and Surface Singularities in Characteristic Zero Book PDF Summary
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 points r = {Ao, AI, A }, 2 and take a projective frame of the type {Ao, AI, A ; U}.
Detail Book of Resolution of Curve and Surface Singularities in Characteristic Zero PDF
- Author : K. Kiyek
- Release : 11 September 2012
- Publisher : Springer Science & Business Media
- ISBN : 9781402020292
- Genre : Mathematics
- Total Page : 506 pages
- Language : English
- PDF File Size : 12,8 Mb
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