{ "item_title" : "Resolution of Curve and Surface Singularities", "item_author" : [" K. Kiyek", "J. L. Vicente "], "item_description" : "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 curvescf.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}.", "item_img_path" : "https://covers2.booksamillion.com/covers/bam/1/40/202/028/1402020287_b.jpg", "price_data" : { "retail_price" : "54.99", "online_price" : "54.99", "our_price" : "54.99", "club_price" : "54.99", "savings_pct" : "0", "savings_amt" : "0.00", "club_savings_pct" : "0", "club_savings_amt" : "0.00", "discount_pct" : "10", "store_price" : "" } }

Overview

Customers Also Bought

Details