{"product_id":"9781402020285","title":"Algebra and Applications","description":"\u003ch1\u003eAlgebra and Applications\u003c\/h1\u003e \u003ch2\u003eKiyek, K.; Vicente, J.L.\u003c\/h2\u003e \u003cp\u003eThe 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}.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2004-10-01\u003c\/p\u003e \u003cp\u003eFormat: Hardcover\u003c\/p\u003e \u003cp\u003eISBN-13: 9781402020285\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-1-4020-2029-2\u003c\/p\u003e \u003cp\u003eDimensions: 297cm x210cm\u003c\/p\u003e \u003cp\u003ePages: 486\u003c\/p\u003e ","brand":"Springer Netherlands","offers":[{"title":"Default Title","offer_id":45580209684620,"sku":"9781402020285","price":49.49,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9781402020285.jpg?v=1775747430","url":"https:\/\/lateknightbooks.com\/products\/9781402020285","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}