We extend the Kuga–Satake construction to the case of limit mixed Hodge structures of K3 type. We use this to study the geometry and Hodge theory of degenerations of Kuga–Satake abelian varieties associated with polarized variations of K3 type Hodge structures over the punctured disc.

The Mellin transform of the fibre integral is calculated for certain quasihomogeneous isolated complete intersection singularities (above all, unimodal singularities of the list by Giusti and Wall). We show the symmetry property of the Gauss–Manin spectra (Theorem 3.1) and shed light on the lattice structure of the poles of the Mellin transform that are expressed by means of some topological data of the singularities (Theorem 4.3, Theorem 5.2). As an application of these results, we express the Hodge number of the fibre in terms of the Gauss–Manin spectra.

Let X/C be a projective algebraic manifold, and further let CHk(X)Q be the Chow group of codimension k algebraic cycles on X, modulo rational equivalence. By considering Q-spreads of cycles on X and the corresponding cycle map into absolute Hodge cohomology, we construct a filtration {F[ell ]}[ell ] [ges ] 0 on CHk(X)Q of ‘Bloch-Beilinson’ type. In the event that a certain conjecture of Jannsen holds (related to the Bloch-Beilinson conjecture on the injectivity, modulo torsion, of the Abel–Jacobi map for smooth proper varieties over Q), this filtration truncates. In particular, his conjecture implies that Fk+1 = 0.