Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Birational transformations of weighted graphs   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.

19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph