Derived categories and Chow theory of Quot-schemes of Grassmannian type
Qingyuan Jiang/姜清元 (University of Edinburgh)
Abstract: Quot-schemes of Grassmannian type naturally arise as resolutions of degeneracy loci of maps between vector bundles over a scheme. In this talk we will talk about the recent results on the relationships of the derived categories and Chow groups among these Quot-Schemes. This framework provides a unified way to understand many known formulae such as blowup formula, Cayley's trick, projectivization formula and formula for Grassmannain type flops and flips, as well as provide new phenomena such as virtual flips. We will also discuss applications to the study of moduli of linear series on curves, blowup of determinantal ideals, generalised nested Hilbert schemes of points on surfaces, and Brill--Noether problem for moduli of stable objects in K3 categories.
Mathematics
Audience: researchers in the topic
| Organizers: | Shing Tung Yau, Shiu-Yuen Cheng, Sen Hu*, Mu-Tao Wang |
| *contact for this listing |