Cycles algébriques sur les surfaces K3 réelles

Abstract

For a real algebraic K3 surface $X(R)$, we give all possible values of the dimension $h_{alg}^1(X(R)$ 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 $X^{\prime }(R)$ 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 $h_{alg}^1(X(R))$is greater or equal than $k$ is a countable union of subspaces of dimension $20-k$.

French, 19 pages, 1 figures, uuencoded compressed PostScript file, hard copy is available from the author; mangolte\@dm.unipi.it

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