In this talk, I will talk about my work on the Griffiths groups of Fano varieties of lines and the second Chow groups of "3-Fano" hypersurfaces. In fact, we give a positive answer to a question of Professor Voisin in some cases. More precisely, we show that the first Griffiths groups of Fano varieties of lines of "2-Fano" hypersurfaces are trivial and the second Chow groups of "3-Fano" hypersurfaces are torsion-free and of rank one. The proof is based on the Tsen-Lang theorem, the moduli space of stable maps, the bend-and-break theorem and the geometry of quadric surfaces in a hypersurface.

海报