RT Book, Section T1 The Nash Problem from Geometric and Topological Perspective A1 Fernández de Bobadilla, Javier A1 Pe Pereira, María AB We survey the proof of the Nash conjecture for surfaces and show how geometric and topological ideas developed in previous articles by the authors influenced it. Later, we summarize the main ideas in the higher dimensional statement and proof by de Fernex and Docampo. We end the paper by explaining later developments on generalized Nash problem and on Kollar and Nemethi holomorphic arcs. PB World Scientific SN 9781786347206 YR 2020 FD 2020 LK https://hdl.handle.net/20.500.14352/97951 UL https://hdl.handle.net/20.500.14352/97951 LA eng NO De Bobadilla JF, Pereira MP (2020) The Nash Problem from Geometric and Topological Perspective. In: Arc Schemes and Singularities. WORLD SCIENTIFIC (EUROPE), pp 173–195 NO Ministerio de Economía, Comercio y Empresa (España) DS Docta Complutense RD 12 abr 2025