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This study proposes DeepWriteSYN, a novel on-line handwriting synthesis approach via deep short-term representations. It comprises two modules: i) an optional and interchangeable temporal segmentation, which divides the handwriting into short-time segments consisting of individual or multiple concatenated strokes; and ii) the on-line synthesis of those short-time handwriting segments, which is based on a sequence-to-sequence Variational Autoencoder (VAE). The main advantages of the proposed approach are that the synthesis is carried out in short-time segments (that can run from a character fraction to full characters) and that the VAE can be trained on a configurable handwriting dataset. These two properties give a lot of flexibility to our synthesiser, e.g., as shown in our experiments, DeepWriteSYN can generate realistic handwriting variations of a given handwritten structure corresponding to the natural variation within a given population or a given subject. These two cases are developed experimentally for individual digits and handwriting signatures, respectively, achieving in both cases remarkable results. Also, we provide experimental results for the task of on-line signature verification showing the high potential of DeepWriteSYN to improve significantly one-shot learning scenarios. To the best of our knowledge, this is the first synthesis approach capable of generating realistic on-line handwriting in the short term (including handwritten signatures) via deep learning. This can be very useful as a module toward long-term realistic handwriting generation either completely synthetic or as natural variation of given handwriting samples.