Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extension of sections via adjoint ideals   The paper contains theorems on extending sections of line bundles from
divisors to the ambient space, inspired by various results of Siu, Kawamata,
and especially Hacon-McKernan and Takayama. Applications are given to
basepoint-freeness, to the invariance of analogues of plurigenera and of part
of the boundary of the pseudo-effective cone in families, and to a simplified
approach towards part of the results used for proving the existence of flips by
Hacon-McKernan.

28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn