Cobo Pablos, M. HelenaSoto Prieto, Manuel JesúsTornero Sánchez, José María2025-01-132025-01-132019-05-30Cobo Pablos, M.H., Soto Prieto, M.J. y Tornero Sánchez, J.M. (2019). Combinatorics and their evolution in resolution of embedded algebroid surfaces. Asian Journal of Mathematics, 24 (5), 725-758. https://doi.org/10.18550/arXiv.1905.12338.1093-61061945-0036https://hdl.handle.net/11441/166463The seminal concept of characteristic polygon of an embedded algebroid surface, first developed by Hironaka, seems well suited for combinatorially (perhaps even effectively) tracking of a resolution process. However, the way this object evolves through the resolution of singularities is not really well understood, as some references had pointed out. The aim of this paper is to study how this object changes as the surface gets resolved. In order to get a precise description of the phenomena involved, we need to use different techniques and ideas. Eventually, some effective results regarding the number of blow-ups needed to decrease the multiplicity are obtained as a side product.application/pdf53 p.engAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Resolution of surface singularitiesNewton polygonEquimultiple locusBlowing-upinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttps://doi.org/10.18550/arXiv.1905.12338