Geometry of superficial elements

Romain Bondil

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arXiv · math/0310129

Geometry of superficial elements

Romain Bondil

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Abstract

In this paper, we study superficial elements of an ideal with respect to a module from a geometrical point of view, using blowing-ups. The notion of weak transform is particularly relevant to this study. We use this viewpoint to get a simple proof of a theorem by D. Kirby characterizing those superficial elements. We also indicate how the same result may be algebraically derived from a more recent theorem of Flenner and Vogel.

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Romain Bondil. 2003-10-09. Geometry of superficial elements. https://arxiv.org/abs/math/0310129

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