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Hironaka's characteristic polygon and effective resolution of surfaces

 

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Author: Piedra Sánchez, Ramón
Tornero Sánchez, José María
Department: Universidad de Sevilla. Departamento de álgebra
Date: 2007-03-01
Published in: Comptes Rendus. Mathematique, 344 (5), 309-312.
Document type: Article
Abstract: Hironaka’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.
Cite: Piedra Sánchez, R. y Tornero Sánchez, J.M. (2007). Hironaka's characteristic polygon and effective resolution of surfaces. Comptes Rendus. Mathematique, 344 (5), 309-312.
Size: 102.3Kb
Format: PDF

URI: http://hdl.handle.net/11441/41935

DOI: 10.1016/j.crma.2007.01.021

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