The curve , is not set-theoretic complete intersection of two quartic surfaces
We prove that Bloch’s conjecture is true for surfaces with obtained as -sets of a section of a very ample vector bundle on a variety with “trivial” Chow groups. We get a similar result in presence of a finite group action, showing that if a projector of the group acts as on holomorphic -forms of , then it acts as on -cycles of degree of . In higher dimension, we also prove a similar but conditional result showing that the generalized Hodge conjecture for general implies the...
We obtain algebraic and geometric conditions for the topological triviality of versal unfoldings of weighted homogeneous complete intersections along subspaces corresponding to deformations of maximal weight. These results are applied: to infinite families of surface singularities in which begin with the exceptional unimodular singularities, to the intersection of pairs of generic quadrics, and to certain curve singularities.The algebraic conditions are related to the operation of adjoining powers,...