%0 Journal Article
%T 2-Cycles on Higher Fano Hypersurfaces
%A Xuanyu Pan
%J Mathematics
%D 2015
%I arXiv
%X Let F(X_d) be a smooth Fano variety of lines of a hypersurface X_d of degree d. In this paper, we prove the Griffiths group Griff_1(F(X_d)) is trivial if the hypersurface X_d is of 2-Fano type. As a result, we give a positive answer to a question of Professor Voisin about the first Griffiths groups of Fano varieties in some cases. Base on this result, we prove that CH_2(X_d)=\mathbb{Z} for a complex smooth $3$-Fano hypersurface X_d whose Fano variety of lines is smooth.
%U http://arxiv.org/abs/1512.01721v1