Birational transformations of weighted graphs

Details Birational transformations of weighted graphs Birational transformations of weighted graphs

2005-11-02

arxiv.org/abs/math/0511063v2

Mathematics

Algebraic Geometry

32 pages; updated 10.11.2005

Scientific paper

We introduce the notion of a standard weighted graph and show that every weighted graph has an essentially unique standard model. Moreover we classify birational transformations between such models. Our central result shows that these are composed of elementary transformations. The latter ones are defined similarly to the well known elementary transformations of ruled surfaces. In a forthcoming paper, we apply these results in the geometric setup to obtain standard equivariant completions of affine surfaces with an action of certain algebraic groups. We show that these completions are unique up to equivariant elementary transformations.

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