中科院数学与系统科学研究院

数学研究所

学术报告会

Speaker：Pan Xuanyu （Washington University in St. Louis）

Title：Griffiths groups and Chow groups

Time：01.04  ,10:30—11:30

Venue：N913

Abstract：

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 answer a question of Professor Voisin in some cases.

More precisely, we prove 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 Tsen-Lang theorem, moduli space of stable maps, bend-and-break theorem and the geometry of quadric surfaces in a hypersurface.

Reference: 2-Cycles on Higher Fano Hypersurfaces (Arxiv)