Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Subvarieties with q-ample normal bundle and q-ample subvarieties   The goal of this article is twofold. On one hand, we study the subvarieties
of projective varieties which possess partially ample normal bundle; we prove
that they are G2 in the ambient space. This generalizes results of Hartshorne
and B\u{a}descu-Schneider. We work with the cohomological partial ampleness
introduced by Totaro.
  On the other hand, we define the concept of a partially ample subvariety,
which generalizes the notion of an ample subvariety introduced by Ottem. We
prove that partially ample subvarieties enjoy the stronger G3 property.
Moreover, we present an application to a connectedness problem posed by
Fulton-Hansen and Hartshorne. The results are illustrated with examples.

11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph