中科院数学与系统科学研究院
数学研究所
代数几何研讨班
报告人： Xiaolei Zhao（Northeasten University）
题 目：Derived categories of K3 surfaces, O’Grady’s filtration, and zero-cycles on holomorphic symplectic varieties
时 间：2017.12.21（星期四），10 :30-11:30
地 点：数学院南楼N913室
摘 要：The Chow group of 0-cycles on K3 surfaces is known to be huge. On the other hand, the 0-cycles arising from intersections of divisors and the second Chern class of the tangent bundle all lie in a one dimensional subgroup. In my talk, I will first recall some recent attempt to generalize this property to hyper-Kahler varieties. Then I will prove a conjecture of O’Grady using methods from derived category, and explain a connection between the K3 surface case and the case of moduli of sheaves. If time permits, I will also discuss some consequences, together with a generalization to Fano varieties of lines on a cubic fourfold containing a plane. This talk is based on a joint work with Junliang Shen and Qizheng Yin, and one with Alina Marian.