Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Numerical analogues of the Kodaira dimension and the Abundance
  Conjecture   We add further notions to Lehmann's list of numerical analogues to the
Kodaira dimension of pseudo-effective divisors on smooth complex projective
varieties, and show new relations between them. Then we use these notions and
relations to fill in a gap in Lehmann's arguments, thus proving that most of
these notions are equal. Finally, we show that the Abundance Conjecture, as
formulated in the context of the Minimal Model Program, and the Generalized
Abundance Conjecture using these numerical analogues to the Kodaira dimension,
are equivalent for non-uniruled complex projective varieties.

13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat