Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cycles alg\'ebriques sur les surfaces K3 r\'eelles   For a real algebraic K3 surface $X(R)$, we give all possible values of the
dimension $h^1_{alg}(X(R)$ of the group $\H^1_{alg}(X(R),Z/2)$ of algebraic
cycles of $X(R)$. In particular, we prove that if $X(R)$ is not an M-surface,
$X(R)$ can always be deformed to some $X'(R)$ with
$h^1_{alg}(X'(R))=\dim\H^1(X(R),Z/2)$. Furthermore, we obtain that in certain
moduli space of real algebraic K3 surfaces, the collection of real isomorphism
classes of K3 surfaces $X(R)$ such that $h^1_{alg}(X(R))$is greater or equal
than $k$ is a countable union of subspaces of dimension $20-k$.

14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
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The categories of this paper are: econ
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an