Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Valuation theoretic methods in the birational geometry of algebraic
  varieties   In this paper, we give a valuation formula for rational top differential
forms of function fields in characteristic zero for arbitrary Abhyankar places
generalizing the classical valuation at prime divisors. This enables us to
define log discrepancies for log pairs for arbitrary Abhyankar places. If the
Abhyankar place has dimension greater than zero we restrict rational top
differential forms with valuation zero to the residue field of the Abhyankar
place, generalizing the classical restriction of a top differential form with a
simple pole along a smooth divisor. This opens up the door to generalize the
classical adjunction machinery to arbitrary Abhyankar places.

10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph