desingularization of curve

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Resolution of singularities — Strong desingularization of Observe that the resolution does not stop after the first blowing up, when the strict transform is smooth, but when it is simple normal crossings with the exceptional divisors. In algebraic geometry, the problem of… … Wikipedia
Pluricanonical ring — In mathematics, the pluricanonical ring of an algebraic variety V (which is non singular), or of a complex manifold, is the graded ring R(V,K)=R(V,K V) of sections of powers of the canonical bundle K .Its n th graded component (for ngeq 0) is::R… … Wikipedia
Nash blowing-up — In algebraic geometry, a Nash blowing up is a process in which, roughly speaking, each singular point is replaced by all the limiting positions of the tangent spaces at the non singular points. Strictly speaking, if X is an algebraic variety of… … Wikipedia

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