Abstract
We consider families of complex algebraic surfaces for which we have a good knowledge of the Néron-Severi group of one of the fibres. Using the theory of ‘Variation of Hodge Structure’ we study which algebraic cycles on this special fibre can deform within the family. For surfaces in P 3 C all this can be made very explicit. We combine this with Shioda's results on the structure of the Néron-Severi group of certain special varieties (e.g. Fermat varieties). As an application we give examples of families of algebraic surfaces for which the generic Picard number can be determined.
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