Cycles algébriques sur les surfaces K3 réelles

Abstract : For a real algebraic K3 surface X, we give all possible values of the dimension of the group of algebraic cycles of X(R). In particular, we prove that if X is not an M-surface, X can always be deformed over R to some X' with totally algebraic homology. Furthermore, we obtain that in certain moduli space of real algebraic K3 surfaces, the collection of real isomorphism classes of K3 surfaces X such that h^1_{alg}(X(R)) is greater or equal than k is a countable union of subspaces of dimension 20-k.
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Submitted on : Tuesday, March 30, 2004 - 5:26:18 PM
Last modification on : Monday, October 29, 2018 - 3:30:04 PM

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Frédéric Mangolte. Cycles algébriques sur les surfaces K3 réelles. Mathematische Zeitschrift, Springer, 1997, 225, pp.559-576. ⟨hal-00001386⟩

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