%0 Journal Article %T Prime Fano threefolds and integrable systems %A Atanas Iliev %A Laurent Manivel %J Mathematics %D 2006 %I arXiv %X For a general K3 surface of genus g = 2,3,...,10, we prove that the intermediate jacobians of the family of prime Fano threefolds of genus g containing S as a hyperplane section, form generically an algebraic completely integrable system. %U http://arxiv.org/abs/math/0606211v1