Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Varieties with very little transcendental cohomology   Given a complex algebraic variety X, we define a natural number called the
motivic dimension which measures the amount of transcendental (co)homology of
X. It is zero precisely when all the (co)homolgy is spanned by algebraic
cycles. Most of this paper is concerned with giving estimates on this number,
along with examples where it is small. As an application, we check or recheck
the Hodge conjectue in a number of examples: uniruled fourfolds, rationally
connected fivefolds, fourfolds fibred by surfaces with p_g=0, Hilbert schemes
of a small number points on surfaces with p_g=0, and generic hypersurfaces.

6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int