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We consider integrable KdV type hierarchy associated naturally with arbitrary semi-simple Frobenius manifolds. Equations defining hierarchy have Lax form and admit bihamiltonian description. This hierarchy is responsible for extension of corresponding semi-infinite variation of Hodge structures by generating variations along higher times {tα,r} satisfying (∂ / ∂ tα,r)L(t)⊆ħ−rL(t).

Semi-infinite variations of Hodge structures and integrable hierarchies of KdV type