Cycles algébriques sur les surfaces K3 réelles
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arXiv
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| Format: | Preprint |
| Published: |
1995
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| _version_ | 1866910963154812928 |
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| author | Mangolte, Frédéric |
| author_facet | Mangolte, Frédéric |
| contents | 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 $20-k$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_alg_geom_9506016 |
| institution | arXiv |
| publishDate | 1995 |
| record_format | arxiv |
| spellingShingle | Cycles algébriques sur les surfaces K3 réelles Mangolte, Frédéric Algebraic Geometry 14C25 (Primary) 14P99 14J28 (Secondary) 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 $20-k$. |
| title | Cycles algébriques sur les surfaces K3 réelles |
| topic | Algebraic Geometry 14C25 (Primary) 14P99 14J28 (Secondary) |
| url | https://arxiv.org/abs/alg-geom/9506016 |