Hironaka's characteristic polygon and effective resolution of surfaces

Description

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.

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Universidad de Sevilla

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Ministerio de Ciencia y Tecnología

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Junta de Andalucía

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