2-Cycles on Higher Fano Hypersurfaces

2015/12/06 by Pan, Xuanyu
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1512.01721

Abstract

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 Griff₁(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 CH₂(X_d)=ℤ for a complex smooth 3-Fano hypersurface X_d whose Fano variety of lines is smooth.

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