Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On varieties of Hilbert type   A variety X over a field K is of Hilbert type if the set of rational points
X(K) is not thin. We prove that if f: X\to S is a dominant morphism of
K-varieties and both S and all fibers f^{-1}(s), s in S(K), are of Hilbert
type, then so is X. We apply this to answer a question of Serre on products of
varieties and to generalize a result of Colliot-Th'el`ene and Sansuc on
algebraic groups.

26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex