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arXiv · alg-geom/9402009

On the Locus of Hodge Classes

Eduardo Cattani·Pierre Deligne·Aroldo Kaplan
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Abstract

Let $f: X \rightarrow S$ be a family of non singular projective varieties parametrized by a complex algebraic variety $S$. Fix $s \in S$, an integer $p$, and a class $h \in {\rm H}^{2p}(X_s,\Z)$ of Hodge type $(p,p)$. We show that the locus, on $S$, where $h$ remains of type $(p,p)$ is algebraic. This result, which in the geometric case would follow from the rational Hodge conjecture, is obtained in the setting of variations of Hodge structures.

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BibTeXRIS

Eduardo Cattani, Pierre Deligne, Aroldo Kaplan. 1994-02-10. On the Locus of Hodge Classes. https://arxiv.org/abs/alg-geom/9402009

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