We study the Chow motive (with rational coefficients) of a hypersurface X in the projective space by using the variety F(X) of l-dimensional planes contained in X. If the degree of X is sufficiently small we show that the primitive part of the motive of X is the tensor product of a direct summand in the motive of a suitable complete intersection in F(X) and the l-th twist Q(-l) of the Lefschetz motive.
On the genus of projective curves not contained in hypersurfaces of given degree, II
Foliations on hypersurfaces in holomorphic symplectic manifolds
On the smoothability problem with rational coefficients
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