Geometry of superficial elements

Details Geometry of superficial elements Geometry of superficial elements

2003-10-09

arxiv.org/abs/math/0310129v1

Mathematics

Commutative Algebra

30 09.2003

Scientific paper

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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