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Let M be a singular irreducible complex manifold of dimension n. There are Q divisors D[-1], D, D,...,D[n+1] on Nash's manifold U -> M such that D[n+1] is relatively ample on bounded sets, D[n] is relatively eventually basepoint free on bounded sets, and D[-1] is canonical with the same relative plurigenera as a resolution of M. The divisor D=D[n] is the supremum of divisors (1/i)D_i. An arc g containing one singular point of M lifts to U if and only if the generating number of oplus_iarXiv:1004.2234v15 fatcat:ialjsgwly5avpl4xt25dcvyeqe