Geodesic
On~correspondences between K3~surfaces
Izvestiya. Mathematics , Tome 30 (1988) no. 2, pp. 375-383

Voir la notice de l'article provenant de la source Math-Net.Ru

Using arithmetic of integral quadratic forms and results of Mukai, it is proved among other things that an endomorphism over $\mathbf Q$ of the cohomology lattice of a $K3$ surface over $\mathbf C$ preserving the Hodge structure and the intersection form is induced by an algebraic cycle (as was conjectured in [2]) provided that the Picard lattice $S_X$ of the surface $X$ represents zero (in particular, this is so if $\operatorname{rg}S_X\geqslant5$). Previously this result was obtained by Mukai under the assumption that $\operatorname{rg}S_X\geqslant11$. Bibliography: 7 titles. 
@article{IM2_1988_30_2_a9,
     author = {V. V. Nikulin},
     title = {On~correspondences between {K3~surfaces}},
     journal = {Izvestiya. Mathematics },
     pages = {375--383},
     publisher = {mathdoc},
     volume = {30},
     number = {2},
     year = {1988},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1988_30_2_a9/}
}
TY  - JOUR
AU  - V. V. Nikulin
TI  - On~correspondences between K3~surfaces
JO  - Izvestiya. Mathematics 
PY  - 1988
SP  - 375
EP  - 383
VL  - 30
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1988_30_2_a9/
LA  - en
ID  - IM2_1988_30_2_a9
ER  - 
%0 Journal Article
%A V. V. Nikulin
%T On~correspondences between K3~surfaces
%J Izvestiya. Mathematics 
%D 1988
%P 375-383
%V 30
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1988_30_2_a9/
%G en
%F IM2_1988_30_2_a9
V. V. Nikulin. On~correspondences between K3~surfaces. Izvestiya. Mathematics , Tome 30 (1988) no. 2, pp. 375-383. http://geodesic.mathdoc.fr/item/IM2_1988_30_2_a9/