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We study special values of regularized theta lifts at complex multiplication(CM) points. In particular, we show that CM values of Borcherds products can beexpressed in terms of finitely many Fourier coefficients of certain harmonicweak Maa{\ss} forms of weight one. As it turns out, these coefficients arelogarithms of algebraic integers whose prime ideal factorization is determinedby special cycles on an arithmetic curve. Our results imply a conjecture ofDuke and Li and give a new proof of the modularity of a certain arithmeticgenerating series of weight one studied by Kudla, Rapoport and Yang.  The results of the paper are much improved in comparison to the 2012 preprintarxiv:1208.2386 which contained partial results in the same direction.Moreover, they are also an improvement of the main result of the authors thesis(CM values of regularized theta lifts, TU Darmstadt, 2013).

CM values of regularized theta lifts and harmonic weak Maa{\ss} forms of weight one