Nash problem on spaces of arcs
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This thesis is organized as an introduction to the Nash problem on arc spaces and a survey of all (known to the author) results, which give a positive or negative answer to it. We start with the class of toric and stable toric varieties (Ishii, Kollár, Petrov), including the original results of the author. Then we survey the class of normal surface singularities (Plénat, Popescu-Pampu, Reguera, Lejeune-Jalabert, Morales), giving two useful sufficient conditions (Plénat) as well. Finally, a couple of results in three and higher dimensional case are observed (Plénat, Popescu-Pampu, Perez). In the thesis are presented and discussed also three generalizations of the problem (embedded Nash problem, Nash problem for pairs, local Nash problem).