2016-06-072016-06-072007-03-01Piedra Sánchez, R. y Tornero Sánchez, J.M. (2007). Hironaka's characteristic polygon and effective resolution of surfaces. Comptes Rendus. Mathematique, 344 (5), 309-312.1631-073xhttp://hdl.handle.net/11441/41935Hironaka’s concept of characteristic polyhedron of a singularity has been one of the most powerful and fruitful ideas of the last decades in singularity theory. In fact, since then combinatorics have become a major tool in many important results. However, this seminal concept is still not enough to cope with some effective problems: for instance, giving a bound on the maximum number of blowing–ups to be performed on a surface before its multiplicity decreases. This short note shows why such a bounding is not possible, at least with the original definitions.application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess10.1016/j.crma.2007.01.021https://idus.us.es/xmlui/handle/11441/41935