1,720,975 research outputs found
On the motive of a K3 surface
No full textIn this paper we show that for a complex K3 surface X with a large Picard number ρ, the finite dimensionality of the transcendental part of the motive t2(X) implies the isomorphism of t2(X) with t2(Y ), where Y is a Kummer surface.Therefore the motive of X belongs to the subcategory generated by motives of abelian varieties. On the other hand, if X and Y are complex distinct K3 surfaces, which are general members of smooth projective families {Xt} and {Ys} over the disk (hence ρ(X) = ρ(Y ) = 1), then Murre’s Conjecture implies that Hom (t2(X), t2(Y ) = 0 in the category of Chow Motives
The Chow Motive of a K3 Surface
No full textIn this note we present some results on the Chow motive h(X)
of an algebraic surface X and relate them to the conjectures of Bloch, Beilinson and Murre. In particular we illustrate the relations between the finite-dimensionality of h(X) and the geometric properties of the surface. Then we focus on the case, where the conjectures are still open, of a complex K3 surface and prove some results which give some evidence to the finite-dimensionality of h(X)
On the transcendental part of the motive of a surface
No full textIn this paper we introduce a birational invariant of a smooth projective surface S over a field k, the transcendental part t_2(S) of the motive h(S), and prove a formula for the endomorphism ring of t_2(S) which is a higher dimensional analogue of a classical result of Weil concerning divisorial correspondences. We also prove
that t_2(S) =0 iff the Albanese kernel T(S_{k(S)} of the surface S over the field k(S) vanishes. Over the complex field C this is equivalent to Bloch’s conjecture ; p_g(S)=0 implies T(S)=0
- …
